{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This is a data simulation that is meant to show several things: <br>\n",
    "<ul>\n",
    "<li>How to simule a bernoulli random event</li>\n",
    "<li>How to build a Logistic Regression using Sci-kit learn</li>\n",
    "<li>Visualize a linear separating hyperplane </li>\n",
    "<li>Use the prior 3 steps to better understand overfitting.</li>\n",
    "</ul>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>First we import necessary libraries and set up functions that can generate a random bernoulli dataset.<br> \n",
    "We input the parameters of the linear hyperplane and get a dataset with $X=<x_1, x_2>$ and $Y \\in [0,1]$</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import math\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "\n",
    "def getP(val):\n",
    "    '''\n",
    "    Get f(x) where f is the logistic function...returns a probability\n",
    "    '''\n",
    "    return (1 + math.exp(-1*val))**-1\n",
    "\n",
    "def getY(val):\n",
    "    '''\n",
    "    Return a binary indicator based on a binomial draw with prob = f(val), f being the logistic function.\n",
    "    '''\n",
    "    return (int(getP(val) > np.random.uniform(0, 1, 1)[0]))\n",
    "\n",
    "def gen_logistic_dataframe(n, alpha, betas):\n",
    "    '''\n",
    "    A function that generates a random logistic dataset.\n",
    "    n is the number of samples\n",
    "    Alpha, betas are the logistic truth, where alpha is the intercept and betas coefficients for vectors.\n",
    "    Uses the shape of betas to determine number of features generated.\n",
    "    '''\n",
    "    X = np.random.random([n, len(betas)])\n",
    "    Y = map(getY, X.dot(betas) + alpha)\n",
    "    d = pd.DataFrame(X, columns= ['f'+ str(j) for j in range(X.shape[1])])\n",
    "    d['Y'] = Y\n",
    "    return d\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for this example we'll generate some data. We let the truth actually be random. We do it this way so we can surprise ourselves with what our models actually learn. \n",
    "\n",
    "We'll also plot it. When we look at the plot, try and guess where the separating line should be?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe0AAAHfCAYAAAB9BoBdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQCAQCAQCgUAgEAgEAoFAoOP8f3oy1Hj3S9odAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ab80b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "n = 1000\n",
    "alpha = np.random.randint(-1,1)\n",
    "beta = np.array([np.random.randn()*3, np.random.randn()*3])\n",
    "#beta = np.array([5, -5])\n",
    "data = gen_logistic_dataframe(n, alpha, beta)\n",
    "\n",
    "plt.figure(figsize = (8, 8))\n",
    "plt.scatter(data['f0'][(data['Y']==0)].values,data['f1'][(data['Y']==0)].values,color='r')\n",
    "plt.scatter(data['f0'][(data['Y']==1)].values,data['f1'][(data['Y']==1)].values,color='b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Generally when we have features X and a target variable Y, our goal is to understand understand how Y varies with X.\n",
    "\n",
    "We can start by just plotting Y as a function of X. Since Y is binary we bin the X features and measure $E[Y|X_{bin}]$.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAGxCAYAAACKkMtSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aef6550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''\n",
    "We have 2 features and a target variable Y. Before we do any modeling, we can group the features\n",
    "and explore the relationship with Y visually\n",
    "'''\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "plt.figure(figsize=(12, 7))\n",
    "#Explore the effect of f0 and f1 by grouping and doing various tests\n",
    "cuts = np.arange(-20, 20, 2)/10.0\n",
    "data['f0_grp'] = pd.cut(data.f0.values, cuts)\n",
    "data['f1_grp'] = pd.cut(data.f1.values, cuts)\n",
    "d0 = data.groupby('f0_grp').mean()\n",
    "d1 = data.groupby('f1_grp').mean()\n",
    "\n",
    "#Now plot it\n",
    "k = len(d0['Y'])\n",
    "k_rng = np.arange(k)\n",
    "p = data['Y'].mean()\n",
    "\n",
    "xrng = np.arange(len(d0['Y']))\n",
    "\n",
    "ax1 = plt.subplot(211)\n",
    "plt.title('How Y varies with f0 and f1')\n",
    "ax1.bar(xrng, d0['Y'])\n",
    "ax1.plot(k_rng, p*np.ones(k), 'r-')\n",
    "ax1.set_xticks(0.4 + xrng)\n",
    "ax1.set_xticklabels(d1.index.values, rotation=0)\n",
    "\n",
    "\n",
    "ax2 = plt.subplot(212)\n",
    "ax2.bar(k_rng, d1['Y'])\n",
    "ax2.set_xticks(0.4 + xrng)\n",
    "ax2.set_xticklabels(d1.index.values, rotation=0)\n",
    "ax2.plot(k_rng, p*np.ones(k), 'r-')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to test the relationship between the features and the target is to use a logistic regression. This is our first look at\n",
    "linear models/logistic regression in this class. In short, we want to fit a line $\\alpha+\\beta X$ such that:\n",
    "\n",
    "$P(Y|X)=f(X)$ where $f(X)=(1+e^{-(\\alpha+\\beta X)})^{-1}$\n",
    "\n",
    "In the next section we fit the model and then we plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlQAAAJPCAYAAAC6iUpxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XecXFX9//HXlvRCEkILvSNIlZKEBEISklBC7733Ioig\nKHrQLyqKKMXGDwQUBGmCgCAihi6oBAHpkEBCKpC2m83uZvfz++PcJbOzs212Zs6Zmffz8dhHsrsz\n975ndnfuZ8793HNARERERERERERERERERERERERERERERERERERERERERKQoVeRgGzOBpUAT0Ajs\nmoNtioiIiJSVGcCw0CFEREREQqnM0XZyMdIlIiIiUpRyUVAZ8CTwb+D0HGxPREREpOysk/y7BvAq\nMDZgFhEREZGCq87BNuYm/y4E/oRvSn825fvvA5vmYD8iIiIi+fYBsFmhd9ofGJT8fwDwPDAp7TZW\n0ESlx4UOUMRc6ABFzoUOUORc6ABFzIUOUORc6ABFLqu6pacjVGvhR6VatnUn8EQPtykiIiJSVHpa\nUM0AdshFEBEREZFilatpEyR/poUOUMSmhQ5Q5KaFDlDkpoUOUMSmhQ5Q5KaFDiD5oR4qERERKRZB\neqhEREQkHp8DQ0OHKBKLKLKVXjRCJSIiUhg65nZde89VVs+heqhEREREekgFlYiIiEgPqaASERER\n6SEVVCIiIhJCBbAM2CiP+3DA7/O4/S+ooBIREZFCmAksxxdRy4AlwObJ1wFuA76f4T7je7DPgjXp\nq6ASERGRQjBgf/wawIOAwcC8LtynIs+5ioYu4RQRESmMmI+5M2g72tQMbAqcATQA9fjRqz8DvwOa\nWDWqdUlyn5HAC/h5pF4F9kzZ3sbA08BS/NrCN9D+Kb+cTptQCNEGExERKTExH3NnABPSvtYMbJL8\n/1bgexnuk1qErQt8CkxJPp+YfL568vmLwDVAL2AsvrD6XTt5clpQaaZ0ERGR8pKLoiub03AVwIPA\nyuTzaVls9zjgL8DjyedPAv8G9ku2tzO+AGsEngUezjJrt6mgEhERKS+hepIMOBB4KuVrzd3cxobA\n4cDUlK9VJ9scgT8NWJfyvY+A9budNAsqqERERCQGmUbO0r/2Mb4n6owMt90Qv45hf3zfVcvXmnIV\nsCO6yk9ERERiMJ9V/VSpX9s05fM78KNTk4AqoC8wDt9b9RH+9N+V+B6qMfirCktGzA1yIiIipSTm\nY26mq/yaWFVEbQZMx5+2eyD52gH4QmkRcHHytV3x/VKfAQvwfVItp/U2Bp7BXxX4BHA9BWpKL4Ro\ng4mIiJQYHXO7LqcFlU75iYiIiPSQCioRERGRHlJBJSIiItJDKqhEREREekgFlYiIiEgPqaASERER\n6SEVVCIiIiI9pIJKREREpIdUUImIiEgpmAlMCLVzFVQiIiJSCDX4JWGWAc34BYxbPj+6m9u6Dfh+\n2teMgDPFV4fasYiIiJSVgSn/nwGcCjyV4XbVwMqCJMohjVCJiIhISOOA2cClwFzgt8CJwLNpt2sG\nNgXOAI5Jbr8MeCjlNjsC/wUWA3cDffKYuxWNUImIiJSWvsCK0CG6aS1gKLABUAUc1c7tDLgJGAXM\nAr6T8r0K4HBgMlAPPA+cBPwmL4nTqKASEREpLbcAx7b7XZeDPiNHRY+30Voz8F2gMfnoivQMBlwP\nzEs+fxjYISfpukAFlYiISGk4Lfn30g5vlftiKBcWAg052M68lP/XASNysM0uUQ+ViIhI8TsE+F7y\n/09CBslS+qhZLdA/5fO1O7l9V7aZVyqoREREitt44NfAfqGD5NB/gW2A7fE9YS7t+/OBTTrZRkFH\n4lRQiYiIFK+d8VezHQ5MD5ylJ9JHk97Fj7g9CbyDv+Iv9Ta3AFsDi4AHOthmsHmp8qGkHoyIiEgk\ntsRPM3Bgytd0zO269p6raJ/DaIOJiIgUqfXwS62cnPZ1HXO7TgWViIhIGVsdeBP4Wobv6ZjbdSqo\nREREytRA4CXgR+18X8fcrlNBJSIiUob6AE8AN9P+FWw65nadCioREZEyUwX8Ebifjifl1jG361RQ\niYiIlJEK4FfAU/g5mTqiY27X5bSg0tIzIiIicbsS2AU/gWdnix4vQkVVVy0KHaC79IMVERHJzoX4\niS3XCB2kjERbt0QbTEREJGLHAR8DG4YOUmairVuiDSYiIhKp/YB5+OVVpLCirVuiDSYiIhKhMcBC\nYLfQQcpUtHVLtMFEREQisx0wH5gUOkgZi7ZuiTaYiIhIRDYBZgNHhA5S5qKtW6INJiIiEom1gfeB\ns0MHkXjrlmiDiYiIRGAI8Crw7dBBBIi4bok2mIiISGD9gWeB62h/fT4prGjrlmiDiYiIBNQLeBi4\nA6gMnEVWibZuiTaYiIhIIJXA74BH8IWVxCPauiXaYCIiIgFUAD8DnsOf8pO4RFu3RBtMREQkgMuB\n14ChoYNIRtHWLdEGExERKbAzgA+AdUIHkXZFW7dEG0xERKSADgM+ATYLHUQ6FG3dEm0wERGRApmI\nX1Jm+9BBpFPR1i3RBhMRESmAXYEFwNjQQaRLoq1bog0mIiKSZ18C5gFTQweRLou2bok2mIiISB5t\nAHwEnBA6iHRLtHVLtMFERETyZA3gbeCi0EGk26KtW6INJiIikgeDgH8BV4UOIlmJtm6JNpiIiEiO\n9QGeBH6DFjsuVtHWLdEGExERyaEq4L7koypwFsletHVLtMFERERypAI/KvUkfpRKile0dUu0wURE\nRHLkKuBlfP+UFLdo65Zog4mIiOTARcBbwPDQQSQnoq1bog0mIiLSQyfg55paP3QQyZlo65Zog4mI\niPTAVPws6FuFDiI5FW3dEm0wERGRLO2BX59vl9BBJOeirVuiDSYiIpKFHfDF1MTQQSQvoq1bog0m\nIiLSTZsCnwCHhQ4ieRNt3RJtMBERkW5YB/gAOCN0EMmraOuWaIOJiIh00VDgNeDy0EEk76KtW6IN\nJiIi0gX9geeAa9H6fOUg2rol2mAiIiKd6AU8CvwOqAycRQoj2rol2mAiIiIdqATuAB7GF1ZSHqKt\nW6INJiIi0o4K4DrgGaBf4CxSWNHWLdEGExERace3gVeBIaGDSMFFW7dEG0xERCSDs4H3gbVDB5Eg\noq1bog0mIiKS5ghgNrBJ6CASTNC6pQqYjm/cS6eCSkREisEkYD6wXeggElTQuuVi4E7gzxm+p4JK\nRERitxuwEBgTOogEF6xuWQ94EtgLjVCJiEjx2RqYB+wXOohEIVjdci+wI7AnKqhERKS4bAh8DBwX\nOohEI6u6paezvu4PLMD3T2k6fhERKSZrAE8A1+An8BTJWnUP7z8aOADYF+gLDMZPz39C2u1cyv+n\nJR8iIiKhDAYeA+4Brg+cRcIal3xEQ6f8RESkGPQFngJ+hc6uSFtBTvnlJISIiEiBVAN/wF/Rdx46\nbkkR0S+riIjEoAK4Gd831TtwFolXtHVLtMFERKSs/Ah4CRgYOohELdq6JdpgIiJSNi4B3gRWDx1E\nohdt3RJtMBERKQsnAzPxE1GLdCbauiXaYCIiUvIOBOYCW4YOIkUj2rol2mAiIlLS9sRPPv2V0EGk\nqERbt0QbTEREStaO+GJqfOggUnSirVuiDSYiIiVpc2AOcEjoIFKUoq1bog0mIiIlZ11gBnBa6CBS\ntKKtW6INJiIiJWUY8AZwWeggUtSirVuiDSYiIiVjAPACcA1an096Jtq6JdpgIiJSEnoDjwG3omJK\nei7auiXaYCIiUvQq8YsdP4Rf+Fikp6KtW6INJiIiRa0CuAF4GugXOIuUjmjrlmiDiYhIUfsuMB1Y\nLXQQKSnR1i3RBhMRkaJ1LvAesFboIFJyoq1bog0mIiJF6WhgNrBx6CBSkqKtW6INJiIiRWcKMB/4\ncuggUrKirVuiDSYiIkVlFH59vtGhg0hJi7ZuiTaYiIgUjS/jR6b2CR1ESl60dUu0wUREpChsBMzC\n906J5Fu0dUu0wUREJHprAe8C54UOImUj2rol2mAiIhK11YBXABc4h5SXaOuWaIOJiEi0+gLTgBvR\n+nxSWNHWLdEGExGRKFUDDwJ34dfqEymkaOuWaIOJiEh0KoDfAo8DvQNnkfIUbd0SbTAREYnOj4EX\ngQGhg0jZirZuiTaYiIhE5VLgDWBY6CBS1qKtW6INJiIi0TgVmAGsGzqIlL1o65Zog4mISBQOBuYA\nm4cOIkLEdUu0wUREJLi98Ovz7RQ6SElwbIfjrNAxilxWdYsuRxURkVC+AvwROAI/gaf0hGM/4O/A\n4tBRJD80QiUiIum2BOYCB4UOUvQcFTguxDEHx8jQcUpAVnVLda5TiIiIdGI94K/A5fgJPCVbjmrg\nemAPYDSOmWEDlS8VVCIiUkir44upXwC3Bs5S3ByrAfcAzfhiamngRGVNPVQiIlIoA4FHgUeAnwTO\nUtwcGwMvAO8CU1VMlQf1UImISG/8yNTNaLHjnnGMxjEXx/mho5SoaOuWaIOJiEhBVAF3A39CrSY9\n4zgGxwIc+4aOUsLUlC4iItGpAG4A1gL2AVaGjVOkHBXAd4GTgAk4Xg8bSNKpoBIRkXxywG74CTxX\nhI1SpBx9gd8CmwAjccwLnEgyUFO6iIjkywXA0fiRKTVNZ8OxJvAU/rTpXiqm4qWCSkRE8uFY4OvA\n3vilZaS7HNsAL+FnPz8aR13gRBKYmtJFRMrLvsA8YJvQQYqWY3LSfH586ChlKNq6JdpgIiKSc7sD\nC0FLoGTNcQ6OeTjGhI5SpnSVn4iIBLUt8ABwHPDPwFmKj6MKuBaYBOyO44PAiaQbVFCJiEgubAI8\nhm9E/2vgLMXHMQg/V1cfYBSOxYETSTepKV1ERHpqbeAJ4Crgj4GzFB/HBsDzwGxgHxVTxUkFlYiI\n9MQQ4HHgd8CvAmcpPo5dgReB24CzcDSGDSQxU1O6iEhp6gc8A1yP1ufrPsfhOBbiOCB0FGklq7ql\nEH8AVqD9iIhI4VTjG9CXAccDzWHjFBG/jMzlwJnAATheDZxIWsuqblFTuoiIdFclcDP+GHISKqa6\nztEHuAk/R9dIHHMCJ5IcUUElIiLdUQFcA2yOnwVdPT9d5RiOH9VbCOyBY3ngRJJDakoXEZHu+Aa+\nkNofVBB0mWMr/NxczwOHq5iSbKgpXUSkNJwOfAiMCB2kqDgm4JiP4+TQUaRLoq1bog0mIiJddigw\nB9gsdJCi4jg9WUZmz9BRpMu09IyIiOTFBPwcU5OA9wNnKQ5+GZkfA1OBsTjeC5xI8kwFlYiIdGQX\n4C7gMNDl/V3iGAjcCQzGX8n3eeBEUgBqShcRkfZsBTwMnIafwFM641gPeBb4FJisYqp8qKASEZFM\n1scvcnwZ8OfAWYqD4yv4K/nuAk7D0RA4kZQYNaWLiBSX4cBbwMWhgxQNxyHJMjIHh44iPaalZ0RE\npMcGAX9PPr4ZOEv8/DIylwLnAwfi+E/gRNJzWdUtKqhERKRFH+ARYCZwBjrD0DFHb/zVjzsBU3HM\nDpxIckNr+YmISNaqgDuApcBZqJjqmGMYcD/++RqLoyZwIglMTekiIlIB/AIYBhwDNIWNEznH5vjm\n8/8Ah6iYkkLRuxwRkbj9H/AvfP+UdMQxLllG5vTQUSRvoq1bog0mIiJ8FXgbWCN0kOg5Tk6KqQmh\no0heaekZERHpluPxUyOMARYGzhIvRyXwA/xs8XvieDtwIomQCioRkfI0FfgJsBfwceAs8XL0B34P\nrIlfRubTwIkkUmpKFxEpP2OB3wIH4CfwlEwcI/BL7tQCE1VMSUdUUImIlJftgfvwV/O9HDhLvBw7\n4K/k+xNwIo76wIlE1JQuIhKJTYFPgMNDB4maY2qyjMwRoaNIENHWLdEGExEpI+sAHwBnhg4SLUcF\njotxfIJjt9BxJBhd5SciIhkNBf6K75v6TeAscXL0Am4ERgGjcXwUOJEUGRVUIiKlrT/wMH6x4x8E\nzhInxxDgXqABGINjaeBEUoTUlC4iUrp6AfcAM4CvoRaMthybAi8CbwIHqpiSmOkPWESk8Crx8yc9\ngi+sJJ1jDI55OM4JHUWiEm3dEm0wEZESVQH8HHgWf8pP0jmOw7EAx+TQUSQ6akoXEREALsfPgL4n\nsDxwlrj4ZWSuBI4D9sLxv8CJpESooBIRKS1nAafg1+dbHDhLXBz9gNuA9YHdcCwIG0hKiZrSRURK\nx+HAFcAkYG7gLHFxrAX8A2gCxquYklxTQSUiUhr2xs+jtC9+Ak9p4dgWeAl4HDgWx4rAiUSyoqZ0\nEZH82g1YiF/0WFI59kmaz48JHUWKRrR1S7TBRERKwJeAecD+oYNEx3E+jrk4RoeOIkVFV/mJiJSZ\nDfFLynwdP9+UADiq8dNG7IVfRmZG4ERSBlRQiYgUpzWAJ4Br8RN4CoBjMPBHfI/waBxLAieSMtHT\npvS++Ea/V/HT9v+wx4lERKQzg4DH8OvP/Txwlng4NgJewC+1s5+KKSk2LbPwVgP/xM99kko9VCIi\nudMXv9Dxr/EzoguAYySOOTguxOl5kR4JXrf0B/4FbJ329eDBRERKRBVwP35kqipwlng4jsKxEMd+\noaNISQjWlF4JvAJsCvwKf+pPRERyqwI/KjUYf0VfU9g4EfAjUVcApwITcLwWOJGUsVwUVM3ADsBq\n+KtNxgHTcrBdERFZ5QfA9sB4oD5wlvAcfYGbgS2AkTjNDC9h5fIqvyXAo8DOtC2oXMr/p2X4voiI\ntO9rwEH4iTtrAmcJz7EG8Cf88jrjcFoAWnpkXPIR1HBgSPL/fsAzwIS026iHSkQkeycBH+EX9BXH\n1jg+wHEVTsunSV4EqVu2xfdPvQq8hp9cLp0KKhGR7ByAnwV9q9BBouDYO1lG5sTQUaSkRVu3RBtM\nRCRiewILgF1CB4mC4ywc83DsETqKlDwtPSMiUiJ2xE+NcDR+Opry5agCrgH2AcbgeD9wIpGMVFCJ\niMRlc/wFPmfjJ/AsX45BwB/w8xyOwrEocCKRdqmhT0QkHiPw0898Fz+BZ/lyrA88i+8hm6JiSmKn\ngkpEJA5D8cXU/0s+ypdjF/xSZncAZ+BoDJxIJApqShcR6dgA4Hngp5T7+nyOQ5NlZA4KHUXKVlZ1\nSyH+cK1A+xERKUa9gYeA+cAp+NUnyo9fRuYbwDnAgTheCZxIyldWdYua0kVEwqkEbgMagdMo32Kq\nN/Ab/NI6I3F8EjiRSLepoBIRCaMCuA5YD5gMrAwbJxDH6sADwOfAWBy1gROJZEVN6SIiYVyBX5tv\nKlAXOEsYji3wzecvAYeqmBLpmJrSRURaOwd4H1grdJBgHHvhmI/jtNBRRNJEW7dEG0xEJICjgNnA\nxqGDBOM4JSmmxoeOIpKBlp4REYncZHzf1ERgRuAsheeoBH4IHALsgeOdwIlEckYFlYhIYYzET1R5\nEPB64CyF5xgA/B5YHX8l32eBE4nklJrSRUTybxv8XFMn4ifwLC+OEcAzwFJgkoopKUUqqERE8msj\n4HHgYuAvYaME4NgRfyXffcDJOOoDJxIpWmpKF5FytSbwLnBB6CBBOA5IlpE5LHQUkW5QU7qISEQG\n40em7gauD5ylsPwyMhcnH/vi+FfgRCJ5p7X8RERyry/wGPAWcC7lNFLv6AX8AtgNmIrj48CJRLor\nq7pFBZWISG5VA/cC9cCxQFPYOAXkGIp/7CuAo3EsC5xIJBtZ1S1qShcRyZ0K/CK//YETKK9ialPg\nRfyUEAeqmBLJvfIZ6haRcnc1/oq2gaGDFJRjLI55OM4KHUUkB6KtW6INJiKSQ5cC/8NPXFk+HCfg\nWIBjUugoIjmiq/xERAI5Bb/g8Rgok0kr/TIy3wOOAcbheDNwIpGgVFCJiPTMQcBVwJ74RY9Ln6Mf\ncDuwLrAbjoWBE4kEp6Z0EZHsjQNuAvbHT+BZ+hxrA9OARmCCiikRTwWViEh2dgLuAY4E/hM4S2E4\ntsM33T8KHIdjReBEImVFTekiUmq2AOYCB4cOUjCOfZPm86NCRxHJs2jrlmiDiYhkYV1gJnBq4ByF\n4ajAcQGOOThGhY4jUgC6yk9EJM+GAU8AvwRuCZwl/xzVwHX4hvvROGaGDSQSLxVUIiJdMxD4C75/\n6MeBs+SfYzXgj8lnu+NYEjKOSOzUlC4i0rnewP3Am8BlgbPkn2Nj4AXgfWB/FVMicVAPlYgUsyrg\nbuBBymFU3zEq6Zc6P3QUkUCirVuiDSYi0okK4Bf4eZf6ho1SAI6jkyv59g0dRSQgNaWLiOTYd4FR\nwF5QwnMuOSqA7wAn4yfrfD1wIpGio4JKRCSz8/Hr1I2BEu4hcvTFX7G4GTASx7zAiUSKkprSRUTa\nOga4FJgELAicJX8cawJ/x7+5HqdiSiR7KqhERFrbB/hZ8u/MsFHyyLE1fhmZp4CjcdQFTiQinVBT\nuogUi9H4EanSnhHcMSlpPj8+dBSRCEVbt0QbTEQkxbbAfGBK6CB55TgbxzwcY0NHEYmUrvITEcnS\nxsBjwFeBxwNnyQ9HFfBTYDJ+5vMPAicSKSkqqESk3K2FX5/vh8BdgbPkh2MQ/rH1xa/JtyhwIpGS\no6Z0ESlnq+FHpO7AT+BZehwbAM8BnwD7qJgSyQ8VVCJSrvoBf8YXG98LnCU/HLsCLwK3A2fhaAyc\nSER6QE3pIhKbauAh4A+U6htLx2E4FuI4IHQUkSKjpnQRkS6oBG4GegOHA81h4+SYX0bmm8BZwCQc\n0wMnEikLKqhEpJxUAD8BtgD2BhrCxskxRx/gN8CX8cvIzAmcSKRsqKASkXJyGX7agD2A2sBZcssx\nHHgA+BTYE1dij08kcqXZOyAi0tbpwJn4gurzwFlyy7ElfhmZF4DDVEyJlCY1pYtIaIcAc4DNQwfJ\nOcd4HPNxnBI6ikiJiLZuiTaYiJSF8fj1+XYMHSTnHKclxdS40FFESoiu8hMRSbMzcDf+ar7SudrN\nLyPzI+AgYCyOdwMnEil7KqhEpFRtBTyM7516OnCW3HEMAO4EhuCv5PsscCIRQU3pIlKa1scvKXM5\nfgLP0uBYF3gWWISfY0rFlEgkVFCJSKkZjl/s+Ebg1sBZcsexE/5KvnuAU3AlNoeWiHRKTekiUigD\ngZfw/UWlw3FQsozMoaGjiJSBrOqWilynyMAKtB8RKW998D1TH+P7por/zZxfRuYS4ELgIBz/DpxI\npBxkVbeooBKRUlAF3IW/0OYIYGXYODng6A38En+l4lQcswInEikXWdUtuspPRIpdBfALfO/UvpRG\nMTUUuB+/PM4YHDWBE4lIJ9SULiLF7nv4UZyDgBWBs/ScYzN88/mr+NN8KqZEBCiFPgYRidWFwDvA\nGqGD5IRjDxzzcJwZOopIGYu2bok2mIgUtePwDegbhg6SE44TcSzAsXfoKCJlLtq6JdpgIlK09gPm\nAVuHDtJjjkocP8DxAY4vhY4jIlrLT0TKwxjgNmB/4M2wUXrI0R+4HVgHv4zMwsCJRCRLakoXkWKy\nHf7qt2PxE3gWL8c6wDR8I/0EFVMixU0FlYgUi02Ax4Dz8UvLFC/H9vgr+R4GTsBRHziRiBQB9VCJ\nSE+tDbwPnB06SI859k+WkTkydBQRySjauiXaYCJSFIYA/wW+HTpIjzgqcHwVxxwcI0PHEZF2aS0/\nESk5/YG/Aq8AX6VY36A5egHX4xvqp+KYGTaQiHRAa/mJSEnpBTwALAFOAJrDxsmSYwhwD9AEHIlj\naeBEItKxrOoWNaWLSIwqgd8m/55M8RZTmwAv4Gdzn6piSkR6ojiH6EUklArgZ8Bz+FN+xcmxO465\nOM4LHUVEuiXauiXaYCISpcuB14ChoYNkzXFssozMlNBRRKTbNFO6iBS9M4FT8c3biwJn6T5HBeDw\nPV/jcbwRNpCIFIoKKhGJxWHAd4A9gbmBs3Sfoy9wK7ARfhmZ+WEDiUghqSldRGKwN/BL/KLH7wfO\n0n2OtYB/JJ+NVzElUn5UUIlIaLsCf8CPUL0aOEv3Ob6MX0bmCeAYHHWBE4lIiVJTuoi050vAPGBq\n6CBZcUxJms+PDR1FRHIm2rol2mAiEtQGwMf4Bu7i4zg3mRZh99BRRCSndJWfiBSNNfCnyH4G/C5w\nlu5xVAPXAhOB3XF8GDiRiERABZWIFNog4C/A/fiCqng4BgN34187R+NYHDiRiERCTekiUkh9gAfx\nix1/O3CW7nFsCDwPfATsp2JKRFKpoBKRQqkC7sRP2HkOxdRf6dgNvybfLcA5OBoDJxKRMlQ8L5oi\nki8VwE3Ak/hRquLhOCK5km//0FFEpCDUlC4i0boK2BEYD9QHztI1fhmZbwGnA3vj+G/gRCISsZ6e\n8lsfPzvw/4A3gAt6nEhESs3FwMHAPsCywFm6xtEHuB04EL+MjIopEcmrtYEdkv8PBN7BT9SXSqf8\nRMrXifgm7g1CB+kyx3Acz+K4D0f/0HFEpOCyqlt6OkI1j1VLRdQAbwEjerhNESkNU4GrgSn4CTzj\n59gKv4zMs8AROJYHTiQiZWgj/DvRgWlf1wiVSPnZA1gA7BI6SJc5JuKYj+Ok0FFEJKigdctA4N/A\nQRm+p4JKpLzsgC+mJoYO0mWOM3DMw7Fn6CgiElywq/x64Wc8vgM/YV8mLuX/05IPESk9mwGP4ueZ\nejJwls45qoAfA/sDY3G8FziRiBTeuOSjRypycP/bgc+Ai9q5jeVgPyISvxHAc8CP8HNOxc0xED/R\n6CDgMByfB04kInHIqm7paVP67sBxwF7A9ORjSg+3KSLFZyjwV+BmiqOYWg/feL4QmKJiSkR6qhAj\nRxqhEilt/YG/AS8BXyP2vknHV4CHgOuAa3CR5xWRQou2btGLlUjp6gX8BfgdxbA2qOMQHAtxGS+g\nEREBLT0jIgVWCdwGNAGnAs1B03TELyNzKXAeMBnHK4ETiUiJUUElItmoAH6OX35qMtAYNk4HHL2B\nX+HXEhyJ45PAiUSkBKmgEpFsfBs/eec4oC5slA44huGndVkC7IGjJnAiESlR8fc8iEhszsav0TcF\nWBw4S/scm+OXkfk3cKiKKREpdmpKFykdRwKfAJuEDtIhx7hk5vPTQkcRkaITbd0SbTAR6ZZJ+CVl\ntgsdpEPmFdP7AAAgAElEQVSOk5M1+SaEjiIiRUlX+YlI3ozEzyp+MPBa4CyZOSqBHwCHAXvieDtw\nIhEpIyqoRKQz2+DX6TwJv7RMfBz9gd8Da+Cv5Ps0cCIRKTNqSheRjmwIPA5cgl/0OD6OEcAzQA2w\nt4opEQlBBZWItGdN4AngGuCOwFkyc+yAv5LvAeAkHPWBE4mI5I2a0kWKz2DgP8D3Qwdpl2MqjgU4\nDg8dRURKSlZ1ixZHFpF0ffHr870DnENsb4r8MjIX4RdiPhjHy4ETiUhpyapuUUElIqmqgXuBBuAY\n/Dp98XD0Am4ERgH74/g4cCIRKT1Z1S26yk9EWlQAvwYGAEcRXzE1BF/s1QO741gWOJGIyBfUlC4i\nLX4IbAscApE1dzs2BV4E/gccqGJKRMpRXP0XIpLJ14E3gdVDB2nDMQbHXBxnh44iImUh2rol2mAi\nAsDJwExgvcA52nIcl1zJNzl0FBEpG9HWLdEGExEOAuYCW4YO0oqjEsf3cXyIY5vQcUSkrGgtPxHp\nlnHA/wP2wU+REAdHP+A2YH38MjILwgYSEemcmtJFytNOwD3AkcC/A2dZxbEW8A/8FYbjVUyJSLFQ\nQSVSfrYAHgHOAp4KnGUVx7bAS8BjwLE4VgROJCISFfVQicRjXWAGcFroIK049kmaz48OHUVEyl60\ndUu0wUTKzDDgDeCy0EFacZyPYw6O0aGjiIigpnQR6cAA4FHgceDHgbN4jmrg58Be+JnPZwROJCKS\nNa3lJ1L6egN/xk+PcAoxjBo7BgN/xPdxHoFjSeBEIiItsqpb1JQuUtoqgdvxS8mcThzF1EbAC8CH\nwH4qpkSkFKigEildFcD1wAj8Yscrw8YBHCPxxdRNwHm4CDKJiBSJ8O+IRcqTA6YDqwXO4TmOSq7k\n2y90FBGRDqgpXUS+cB5wLDAGAp9Sc1QAVwCnAhNxvBY0j4hIHqigEik9RwPfAMYC84MmcfQFbgY2\nB3bDMS9oHhGRPFEPlUhpmYKfimAKBJ6GwLEG8CT+KsNxKqZEpJSpoBIpHaOB3wMH4yfwDMexNfBP\nYBpwFI66oHlEREqAmtJF8u/L+NN7+4QOgmPvpPn8hNBRRESyEG3dEm0wkRKxMTAbOCZ0EBxn4ZiH\nY2zoKCIiWdJVfiJlaC3gCeBq4A/BUjiqgGvwI2RjcLwfLIuISAAqqESK12r4tfnuBG4IlsIxCF/M\n9QdG4VgULIuISCBqShcpTv3w6/M9D1wZLIVjfeA5/DqBU1RMiUi5UkElUnyqgbuBOcAFhOpTdOyC\nv5Lvd8CZOBqD5BARKRNqShfJnQrgVvypvt7BUjgOw7EQx4HBMoiI5Iea0kVKXAXwE2ArYCLQUPAE\nfhmZbwDnAJNwTC94BhGRCKmgEikel+JnQN8DqC343h29gZuAbYGROD4peAYRkUipoBIpDqcBZ+EX\nO/684Ht3rA48kOx7D1yAgk5EJGJqSheJ3yHA94HJEGBUyLElvvn8n8ChKqZERMJQU7pI9sYDC4Cd\nguzdsReO+ThODbJ/EZHCi7ZuiTaYSOR2BhYC44Ls3XFqUkztFWT/IiJh6Co/kRKyJfAwcDowraB7\ndlQCPwIOBsbieLeg+xcRKUIqqETisx7wV+BbwIMF3bNjAHAHMAx/Jd9nBd2/iEiRUlO6SFxWxy92\n/AvgtwXds2Nd4BlgMbC3iikRka5TQSUSj4HAX/Cn+n5S0D07dsJfxXcvcAouwKShIiLSITWli3Su\nD35k6hb8jOiF4zgwWUbm0ILuV0QkTlnVLYV44bYC7UekWFUBf8CvzXc4sLIge/XLyHwN+CpwMI5/\nFWS/IiJxy6puUVO6SFgVwI3AmsA+FK6Y6gX8EtgFGIVjVkH2KyJSolRQiYR1JbArsBewoiB7dAwF\n7gOW46dFWFaQ/YqIlDA1pYuEcwFwFH5kamlB9ujYDHgR+C9wkIopEZHioaZ0kbaOBWYBGxZsj449\ncMzDcVbB9ikiUnyirVuiDSYSyH7AfGCbgu3RcQKOBTj2Ltg+RUSKU7R1S7TBRALYHb8+38iC7M1R\nieMqHB/g2Log+xQRKW5ay08kctsBDwDH4SfRzC9Hf+B2YB38MjIL875PEZEypaZ0kcLYBHgMuBC/\nTl9+OdbGL6pcD0xUMSUikl8qqETyb238LOj/B9yd9705tgNewi9hczyuQNMxiIhIXqmHSsrZEOBV\n4DsF2Ztjv6T5/KiC7E9EpPRo6RmRyPTDn957FX+qL39vLvwyMhcAlwGH4ArQoyUiUpqyqltUUInk\nRy/gfmAZcDzQnLc9OaqB64E9gP1xzMzbvkRESp/W8hOJRCVwC/7v62TyW0ytBtyT7GM0rkAzrouI\nSCtqShfJrQrgGmBT4DCgIW97cmwMvAC8C0xVMSUiUtrUlC7l5JvA68DQvO7FMRrHXBzn53U/IiLl\nJ9q6JdpgIjl2BvAhMCKve3Eck1zJt29e9yMiUp6irVuiDSaSQ4cBc4DN8rYHRwUOh2Mmjm3zth8R\nkfKmpWdEApkI/BKYBLyflz04+gK/xc+4PhLHvLzsR0REsqKmdJGe2QW4Cz9C9Wpe9uBYE3gKqAL2\nUjElIhIfFVQi2dsKv7zLqcAzedmDYxv8MjJ/B47GUZeX/YiISPTUQyWlaAPgI+DEvO3BMTlpPj8+\nb/sQEZF00dYt0QYTydJw4C3g4rztwXEOjnk4xuRtHyIikoma0kUKYBDwF+BB4Nqcb91RlWx3ErA7\njg9yvg8REck5reUn0nV9gEeBGfg5p3I7+uoYBNyd7OcwHItzun0REemKrOoWNaWLdE0VcCewBDiL\n3BdTGwDPA7OBfVRMiYgUFxVUIp2rwM8zNRQ4FmjK6dYduwIvArcBZ+FozOn2RUSkJKgpXYrdVcC/\n8P1TueU4HMdCHAfkfNsiIpINNaWL5MFFwKHAWGBZzrbqqAAuB84E9sblaVJQEREpCBVUIu07AV9Q\njQEW5myrjj7ATcA2+GVk5uRs2yIiEoR6qEQymwr8GJgMfJyzrTqGA38DBgJ7qpgSESkNKqhE2hqL\nX4j4APwEnrnh2Ar4J/ACcDiO2pxtW0RESp6a0qWY7AAsAPbO6VYdE3DMx3FyTrcrIiK5Fqxu+S0w\nH3i9ne+roJJisSkwBzg8p1t1nJ4UU+Nyul0REcmHYHXLWGBHVFBJcVsH+BA/aWduOKpwXIPjXRxb\n5Gy7IiKST1nVLbnooXoWWJSD7UiX2L5gH4AtBLsFrG9B9grjDF40eM3gIms1Lb9VFipH11gfsK3A\n1ujiHYYCf4XV7wL7Y04iOAYCDwA746/kezcn2y1aNhjscrBfgh0UOk2xMdjK4ECDrUNn6S6DCoPD\nDb5tcLCV6VJkBv0NbjL40OA5g+1ysM1Kg10NJhoMyUVOCW8jNEJVALYjWC2YgVkVjfWb8t6T5pdF\nyd9eYWeDWmvZMdQYXJZ892ywFWBNYC+DrdnDffU2uM7gI4Pp5kdAM92unRdl2xpsPtiyJJfrZJf9\nofIFOO4jWFkPzQ0VND0A1ivLR7Azq7/9V87bYhlnbzsNR+8M2TcwuNXgMYOzwh5gbF+w18DeB7vC\nF8c93KI/gA5Z9bhsQLL9+uRXqBbsm+3cr1+pHHANdjD4nsE3DNbuwXbONVhusDj595Jc5swFgwEG\nVxm8avCUwejk6xUGv0teM5qSf3+Vpwz7GXxgsMDgZoO8v8kzWM/gRoM/GhzRyW0fMqhLXkObDZYY\nrNvF/Wxm8A+Djw3uMxhmUJ28hixLfjc+Mz8Vi/Rc0LplI1RQFYB9C2zlqrrGbBBLzOBpgywLgC7s\nFX5uqTv1Hx+BjU0t8MAawKb1YE+7fJOrnvsLU1Y0r9pobeq7coM1DJ5NXpyXGByZto33wFLubjVg\ne7azw17Ao7DHW9XUffG89qW2+Vh+/7TBZQbrdyP/tox4eTkXr2vs/iODplqw01rdAtY0+DTJbwZ1\ndfT5AdjPwRYnI4/nd32fPWGj035+tWDf7dEWYU+DRQYNyeMclRTdqT8TS4rdCoPtDO4xP/q5OHle\n5vv7FS+DCcnvbpNBffJcdOngmbadNVMOwi0fdd37vcyv5GdYk5axNikot0yKwDb5jbZvNnqQ4Stp\n+1lucGuutt/OPtcyWGjQmPKYL27ntr0MVmZ4Hm4x2KqT/ayWFIktrxn1Bq8YnJL2vDcbTM/Poy07\nURdULuVjXAHylCi7AKwu9W9yLea0jBilXD1mfcH6d2vL/g9+V4Pd0l/oDH7c8sfcDFZDf2ui4j2w\ny8Aa0w6UdT14bLX9qLEBLLPjub3lCNxgcGlKlmeSr6W+cO+UfLcyw4G7rp0CpRK4A3hkdWbPSK8X\n9+avLftebL5ZvXOjfvIwXx9ufOn+1G21OtVncHbKC6MZ2OV8f2WGwubQNs8Q7GVwf1KA5KDgsBva\n1sk2M+ut+XfNy9I2uLiSla9m2I8NYNm/F7FaTXIgSL/BEoPBPX+MYZgfqUl9PI0GV2exnR2T56LV\nc5qbn39uGLyf4efXbPAzg5FJ3vRia0lym/eNtv2FSbHydFJ0zDIY30mGK9L/roz8LjBucKHBirR9\nft7ObVezVYVX6seK5PnYv4P9TM7wO1BncH2Gvx0tqp6dcbSuUyxcFI1QFYgNAZvVmzqroMn6UWN3\ncpQlLyTJ6Rq7CT+K1Qj2CFi/Trfq/9hfSw6GS19nm/cGsOwWsNvBJpgfbl76NyY0DeFzq6LR+lG7\nCH+KqCbtNWJWFo9rAKtOB7UcbO0ldml54Tg/yTkuwwtIncGFKduanZZnGdiUtB1WwEZ3wuaz4bNr\nt2P6B9UpNVpvVti5XN+ygZXmFy1uX7+FAzn7y9dy2dAa1vlXekH3Xtpz/bP0F9WteDPD66zdlXa/\nydb6tGutJadVuvQM+5/hpQYXG4xIvno1aSOeYG93Y5s7GrxsvifkpwajMxw8l/RmRfrPxMCsioaV\nR/KHtt9YVTTs0tUssUmek/THdFOG221nsI/Bccl9PjP4vUF/gEO5d4v9eLhxC962o7nDPmdIyxuo\n1Qv/qNoyf0ovvZBpKah+YjDQ/ChOy99tU9rfcLP5gqkybbv/ttYFSI3BJsnv3Hnme7KqU25/kbUd\nycvrpLkGX7fWb+7MYGmG2+1k8HmGfKkf7a7EYLCHtX2jUm9wkrUeoWo0eDqfj7mMWKgd34X/xa0H\nZkGbeXaCBStNNvQyfvj+pfyo6WnG2ptsZaN5rqkftfPwPUypIx3Lwa5rZzt9wMaBTfg2Vz65OW83\nb8L7dhk/sIEssYpVr5G1YIfcxGmj+1CXPhr1KdgLSdGyLLnthIx7g13MF20LzI+ypDRQ2npJ1i+2\nvRqL7M/sb+aH7oebL6Zq015ULHmhOaZlS2sxd0wv6uv6UFdXycoV+AKzpZenCmxDGHUbbNvkz0xZ\nczUN9Wsyt3kwi20QS2xz3mk5cLV8PNruj2PAvAkcdGIDZ23XxOCP62ldGNaCnZH2PJya/hhG8Xx6\nEdYIdkPa/Z7O8Ngf6PBXZdV9dzKoWUHvhm9wVeNonmscxqd34XvyFqcUVbVgh3Rxm1+xtsXtm5bh\n9E5/lj2EPx3c5iGsx8ftHWDqDDboSpZ8MN/nNtJgqMEog5nmRxNe7kougx9a2wJ4ctptfp58fWmG\nx34XWD+wjypoWklS6G/PK1ZPr2Pz8IjXAduObo5sJ48jU/HYkPyu97qO8/cawzPLRjC7eRx/Xz6L\nddNPD9ZZSo+Z+ebt9NNjSw1+lTxfy5O/+39Y0j+a/JxmJz+j5uR2R7afuufMn3JLLSZrDW7swvPT\nZG2L0JUd7Kfa4KWUv61a8z1iFeb7TeuTr71nWZxWlowsdID2RBusWJkfDn91Pms0DOFzg6aWA3JT\nhmPT68l99jR4weC1D9noW9D8FthSX8is+tv2IzVt3nC+6QslW5z29WX4q+kOADsJLOOpMfONm6nv\nsFYYTEu5RRXYJ6ScrhvAMpvNiJYXj5MNHs3wor3SfO9Nr2Q/vQxe+pRhtf9gz6bX2Wa5wTnJPjYG\nmwk31Ps3unNSNtPcPJEn5j7CvnWPM6l+OX1TC4Uag+My/iBO33lNTtpjJUcdYPT2D6+ClfXrMuvN\nQSx5GazN/QzWsdbvKpv+wZ4zobkmKaTqwT4DWy/tfs9lePx/buc3pCLtvn83aJ7Kg9YvOcZX0dgE\n9iHYl8CuxReee2Xelp0D9iLY42A7J9t8KUMeM38VU01yAKw1+DrYcLD/kTYKCc3Nu/FC+i9byymQ\n72V+bN1nsK75UaBtu3j7bxvUvcDIZZdwdYPjioZ5rJn6O/eeddI4nxwEf2Z+dGaW+XUhU78/2tr2\nHaV+1ICNgaalqV/uT429xZYzLMMV2gZrGzxg8K7508LDu/gMfRff07Yk+d3bsWv3+2K/Y631SE1T\n8ve+bDl9/1NB00d80RrQtHIjPmyup1fqY623lAZyg6rka+lvnNJPry0zOCjlfsPMj8L+0Nq5mKWd\nRzAM7Ptgt4Edmf73085jHmWtC+Ymg2mWYX1ca1sc1qc9vgbzqyd0tL++yWO7xXyhWpnyveEGG1ue\nL04qMxY6QHuiDVbsRjD7RGheSruvybYS7GHzowm1tfSzOvrY2fyioYrG9FM9HX28j796bnna11eA\nDYEvXgQzvhCZP52RPmS90lpdhWNbgr1bQZOtzkJ7kvGpt/2lweMZgr1hKc345i/JTt/PCp/LXoG7\nm2GEZWr5WIu5z5k/bXCowTUGn33Mep/exZHXDuWzQcn2t04OVE88sBVf54rqD5h8USMVq14vB7PY\n7ufguuTF9qR2no+R5q9GWm6+IFwPX5h+E+xrYG2uCDN/iiN9xGNS2q12AJuBL6xn+M/B4NXPGWK9\n045HA1nSfBdHvmJ+Dq7UfQ1PfmdWx/fJpZ7WrQHb2uCtdn5ZDjR/Veix5uena9lqNdhXwN7GF/JL\nwBbdwLmnmi/OZprvj/tV8vO+zHwrQbcZ9EkOOt9KtlNr/hRircFPO7nvjga1j7KP9U8uTOtFvQ1n\ngc1lrZbH2GpEJcuMx1rbkanUjwVgu1bR2Opvri/L7SPWb9OU/hBT+81jzRkrqWwpbOoN/mcZDvBp\nSXan9ai2gXVr7UqDJ61tAWQG9jI71/VmxYq0x9A4ne1rzReUtQZnZtjmucn3GpPbPWdtR0RrDE7v\nZtZe5k/V3WvwnRO4bTjYTFYV+zVgV3RhOzdkeLwz0m4zzHwhPyste43B1bbqooWXzRfD+xjMNf/a\nuNz8CNyG3XhsKqhyx0IHaE+0wWJmfvqAsw1+ZHBgO7eamhycWv1dV7Kypg/LGwaytO4mTjt0MYOv\n25+HrJoGq6LR1mF2B6/jZhWt31DV+IMq4K9Eq2HV6b2vGgw2X+ysTA40F2R4LAdZ20KnMdMLwAp6\nP/cKOzTtzrO2Ke/Z2dzYsIjVvmowxdoWFFPT9nOytX3X32TQGx5r8BcIpvcKm/WhbuXdHFFn/qC7\nzGA0/orKlnftiw/jnkOSA2DztA2xNS+h+eT9e92TPBdfbKs/NfYGW6cWc3168FtQiR/dqUwe3xHm\ni4/nzRd+qXOBDQT7PO2xfQY2wOBbnzKsJr2gGsRie4zJZr64azl1ckzyYr7EoLYftenbbAK7yuCC\nDL88Tdbp6TDrg5+q4dDnGH2Mrbqc3lIOOivNv2tfYp1cAdVm6/6A+a/k9yN9ZKDlYLZrB/c/ymDp\nlmn1YjX19m2+lzqi0O1TY2n72dbansJutlWnq44Fqx7M4jf6Jmd6+lNjU3nQmqiot9anzCdW0VjT\nmxU2lM/seUa1bG+ZdTpvlZ1B24KqmS5OG2L+tFOmZmszsP/xJevNilatApWsXHELJ59kcJp9cUFJ\nxm3vYX7KiROSn2t6X1Vt54+vTdaHU5735ddz3rvQvCwtdssVqH3NFzqZRgOvzvD79XbK97cz31PQ\nUsg3JK8fK5K/37eSf1uml9i6nd+HueYXUu/ocW1h8E5y+wUGGUaapZssdID2RBssVuZPFzyf8gdW\ns4wB/weWVoBYX/yplJZ3gDUjmHXnfRxSdw+HNX/GUDOoPZy73+mX8rfai3qror6ZNq/j/kX7h1xq\n2zO9uZKV74JdQqshcBsDdiLYTknWe631UHytwZS0x9PH4L+2qimz1iDju8AruWLMQJY2txxje1PX\nVMnKu5Pt7G++l+gZy1BkGmya9qJUb34ofTcY1uTv1upFc8FAls77Dae1ahZ9jtFz0g8yA1hW20TF\nylt3wNa8BHtyY8zgE7ApYDW9qK/ty3L7EZemviB2YSTD+uBPu6XczjYAOx5/inUF2CKwsclj3Nlg\nXvJi/pnBHsl9dsEXf6kPZQnYTuZHD386mccaW34Pqqm3DZhpNfRvKW43Sw4erXqgRjA7vb9rJdj3\nkiw3p3yjyeDgjh9rq5/V4AwHkEwF2r0p9xma/A5MtHYuuTc4xNoW76kfSw2O6iDXDga16zKrzV3P\n5fqWeZQu7+rj7OQ5OCv526kxP63CT83P5fTF6apt+W//s7nxvYN4oPFqLrEGqhsN/mKr5vgaTtqF\nIauxqOXnutw6vULVxqXfH2xuhqy7mG8ZeMP8KdGqlO+lX4hgBlZLP/sb4+t24l/1/ZL3Of2psX15\nuLGG/p2O8CW/txOTn+na5k+Xv5T8XiyylNN9XWGwoaWdNvw1ZzRWsrIuLfrKBqrPSV4/6szP/bR5\nynYGG/zJWo861RoclnKbVzN835k/JZ4+p99W5kfk2mtav7KT52i2tR0BG9Gd50basNAB2hNtsFgZ\n7N1yUKihv+3LI1ZFo0FzI9gPaF3gDML3QNwGdlITFTen/XHZFryV/oJhw1jYWE1DUwVN9WD/PIAH\nXz+LXza8yG4tp6suAhsF9jTYdLCLydBbkBwI0t9V/TjlFquBTdyAmeNW0Pti830l7Yy4AdiZ0Jx+\narEx077bee7Gm58UtMbgiSn+HeA8OOwi/Gje4uQAch9YpWW4UudWTmwkbeSpoqKh6aIJvZo3vQB7\na/gX30iuIrI19uPhQz9ko+Vpz8Mn1uFqBLaFP3jZUnzh9BOwe0ibGiP5WHoGv17L/NVC6QXCMLCN\nMtyvDixlxMj6nM2N80fxvJ3AbTafNVILl3Usw1V613JhXcoBpzl5XlodpM1fydWtyTgNtrGOT3m1\nfDyV3H4z8/1IS5L7/ddgQIbtnmod9yZ1OqphcOmF/Kwx9U1IFY31N3Durw0yXnSRLYNB5vtf2h0R\nMj9a/Z6tGp1JmRzTxpLW2ziIJfYq2y03P+ljF34udi3+dP5ifBHeakoGa3t1baPB9SnfP9ZWjcLU\nGNTOYe36DZhpfVleP4Cltg6z7Thutxs4xxqoXmKdFEPJY342eR1s+Zl/JfleVhO/Gmye/tr4Eetb\nNQ11rOrfXL4m8/5ubfuj3km2UWn+4pr036vL0vaV/ndq5nu70ovPRoNvGhxt7b/BqLN2Tn+bn88r\n/UKQxdbBNAzSJRY6QHuiDRYr86dzlhjYKdxsfVv/vdSSodk55b53pf9BjudvS0iuFAKzXqyw87jO\n5rJW8yzWXVZHn43ND4dPMDjdYFewbWk9SpOxt8Dg7ZYbNFJl13BRw/ZMn44v8rbHT1S5ODkQTwPr\nZDI/O4m275gbyOLqI3z/wcfA8cm2h4NNxo/mVCT59zKomcW69geOsofZr+lx9n6r1WPvVWsceUDD\n6FNoWtD/ixfkGoNvpD0XU5OvN5ov6jo73fIGrS8kWMGq0cZWHxU0Lf0tJ/2ftS0WGg2+mmzvZ8lz\nV5f826ZfyPwISHoj+PTke+tkeHFevi6zzgB7DOwusJwsfWJ+qo70faV/1Bickdz+72m56yzDKKf5\nwiv1wNRgq/pwVhic1jZNW6+zzfob88EfKmhagO+x6XAW7Hwyf0FJpsvmh4BtQlpvYy/qm/7Hl660\nbk32a5vh+6naLF9iZBiugxVpt9nNfNP0KQZ9+7L8QWj+4srOPtTZJVzdct9l1sl8hAZnWtsC439d\nfzwZt9k3w+Novp3jr8JfdDED7NfzWeO8DL+bzeZPO25lmU9xpp7u29nazhtVY/51fWH682jwNfOj\n+NMt82nqFdZqaphWj2mg4U833MC5thnv2ua80zyev32nJ8+VxFu3RBssVuaHt5cY2EZ8kOlYc1s7\n96x4nElHLGZwqyHlpxj3HbAFYEsHsrR5Iz60TxmWesD5RoZt/YC2k2S2mdfF/BU+NQa1h3BfY1+W\nt9yn5aCeWjDUgl0J9gzYLLD7wdLm07HV8HNJpfZdNOKvSBtg/h19h0WZweGfwCsbQt0+cEva9yba\nqsbPfxusfxsn/HIgS20gS2wAy5r7snw62FVgdQyavYQzdmriqxs8/uEQdjX/rv8F8/1tmUbsKgwG\ndZQv5dZpV71lvEozOSAtt9mMaG9Ep86+uCTfJuInSZ2Ysp8BJIWs+Xf+DyaPv9l8v1FqY//x1nqZ\nk8O79li6z/ypnJbm5GaD/8/edYdZUWTf8yYHhowIggkEFVTMWVFXBROKadVVDKtijqisacwJFWXF\njDmLOa4BMWcxkQQxkOPMvBzP749bPa+6uvq9NwPuzOxv7vf1N/C6u+p2dXfV7XvPPTc2Bxv+ejFu\niJ6F8dHJOOQJKlA17an5j/m06/JSUrA6UfWsz2cbq4dHASvbiB1VMgGvUO9Wvfp77hru38yuI4Um\nJ9dZP5inDMdrGXVP3mWeOrIUw9/ss8mklRSPUjf1N0CvhyhEL53FcZa+Q2rfANoNqj/U/vXpNX7T\nlHBugMBZzBqKSUrYfigl5PcPCseWjdcrSh8jlMB5E3FqvMpNmh5Ge83M1RG2tAJ+0moVa80yAwN3\negEH/zYQM1LG+xWDwrC4hWupSSwaQDp1MCav2htvBdfFvDkBpEcD7ALwsOdwaIPCV+gGlQM67wdw\nOwjA+Wp4SR+t2T8E+n2JbS4sQsrkqTINMkIMLcdwiAP8Fp5wHrvDA7DOcDNMa0gj4HgcrvXRZWQd\nEIEVdxQAACAASURBVN4agiqnxkKsJjuTCG86JPNM1zEMcDRGHjMcl5UvxsWdr0HtX1FfjnOMMTJ5\nrAhkUpUI82ZcYLe0stt7lvY7QUK2SbXdEEV5P4onbVv6GH4UWo7tCViKS7MEkon4MiRE2cmnDYc2\nYCnFw2H1qlIyBXYk0Avg+kBmVRFSGSDNSoT5KvZfRAkPzqMXk3KKrU2j/WHGeU4o9r9eL5CCd9mT\n4qmwYFy4NsQg3sQ4rzPd5YriFG+GHvrfEpLyP/gv0Pt7y/O2goJj+ozAhpaz7ocWgi5CMvZ3PPku\nhYwyT+YhdG+vPk/9p4l670ExROOUENzOBA5T/48pI+ULSnawThJ6tfHMkMAita+IgiMzDSYHVzia\nXu9WUr9X6v4/RckUPFkd73BrfUoJodqMts/9rrUj6n62TAuvNmW82sUlbGkF/KTVKtZ6hd3UYtsA\n8fJk1F9n+wiSnaNPqG/AS57oLNZhsS8ASokGZ6JKE6iPonx9gPdAQgf1EMLO4erfaa0NS4oyayCG\nWH94aRUIt9clajkmCrCXpd0VZluliPNt7K1/WXpIKEPA1D0AngqXpfKWuvajaOB2FqFnAkibIcYM\ndrrlGdRiKWpzFzxdPeGWEMB5nRrfxwBOUfe4HuCSdfDnxd9iiOkhsIUFpljafwZaCLEEidjjODrG\nrPfpMgh55HmQcKELVK4Wj/MIfFSPmhdfxf5bQcJ+Tjg0BuEo82QyUrJT89A8eM4aD6RdXrot8B2Z\nzY7Sr/dh5vdyBGjHssRZMEeTp811CYxSC3Oe4rvsCqGK6E4xMN9jFhMUpKt8DPdR971OvSOuMjWU\nmnifUAjUXuJ/kSmdEkZdQjSS1MWZNe5SFAPVGAvWQEh/I+o5eQUqc5ACDt+deYDTBK5SfcYpIO+C\nC6/TXgapQY1fnFmDKaqO+5hZPrtXLc/MMm1/JYFX1LkhCiO8kyV7PL1heUXdYtVzhXFsUM1TL1t0\nyBHy5BT3oWmWI/p8oePVLh5hSyvgJ61WsdYrnAi3pyIJ8eTo4MkQQC1Ux2Xe98+1LQUaF5nRFI6T\n5wlsDPAAuHFLGYCzIaDphwC+AEttOYCj1WQZghhhM+ANW2Ughl4c4tUwU5QTALtY2n7OvIZyRDkR\no/UfbzdOKtkDWHIYPK61V9UCeD+1r8encIQiusxonrUMseMtcVxasRy12H4N3lQfYSeAu66FxVsQ\nmJhC0arPsd2yW3HetQCrKEaNDXehZwT51ALLLDTH8FRM5DJ0YwxljKEsUoHIdGSN3BDAxowiAjem\nEQidhTtYggRLZB0yvY4NUOFFCoHmvWoxMHUmgXvyjMVD5in9Mdv2MDcQ2C/vyAqfllkaxDGoCvGS\n9KQYUA5txbZqwXO2n6gB4ykkZy8SmDEBZ0xRyRX1ACP/xL33WBbaOerMogDS5nsRBuhL7/DfFgr+\naAuK58gMP9YTGGI5KwCwL7QPJkpIywkphwkcSTE2d6TQJFRa+u3Kpic92MogOWFf2zOVUfun0B7i\nTFAgAjlLeVEyAE3MWYISRnyQQoL3PsVADtBO+vk8gSvp/SC5m8BrlDD2CALVznPcAQ1Ds3CLNKsR\n5OfYbibbuamaK2xpBfyk1SrWeoXvWd75P+EtRLxUO+cb2ENsjcdSih+/rF5IzbvDqyznJvLoOAhe\n/pplEI+L2fe7kDBeCQT8qS/gnvpmqv0as/0qhHSOnQjdQM0AgAd6AF9HvVXn32MWLJ4iEF+OrrFK\nE/NalCAOOCWNC3ouQm3hhHprQijhMatHh7KQr1DXEKVksg1TE/MUCn3BHxRyzNEUgOvkbfBFRg8X\nlyHKbljKckRZijiPxcNxkzhSPWMObin4EI5jletD31PHuB7gMErobimzoQoTB5KkGLQPqQVjf8so\n7F2MZFy/37W43O+BnlTAmJbQnoqeE7BLCc09Q1lYIwS+oVA2mNldUQIXqnOqKLit5Cp0ovlslSGW\nWoBe5uIZAoCvsdURpV5ezAaARzX9SWq8hn6UD4nvKMXN8ySDFNzuAFoSF1hAAXGKZ8p27rfMeu5+\n52qn/DOwMaaP2QGfpPfBm/wM2+vPoK0Qt2n8+B0TIXB+Add5Bb2GUlR7FtMUz2l3SiajaeTF1Hh8\nSMEOzlfvjpl56LxjIQIPf4Ftw6fhLp6FOxwuvCALrA7QLh5hSyvgJ61WsdYrvBzemnwfw4tp0g2q\nQRDckUMLkILmzRqMH+40XsjwSzjofAin1FLL/DE7j45/h9fAy8DrKYsCvFE7rwLCbXU/wBOQkw6B\nmwJcDDAUQDpxDS6NUrwTDZSvRT3McAOALyFZL7tSGM2foYRnPJlxz+HQCcVIZr1yFauI4/ZM4sKe\nn6EWHZtx01ZL1EJi3oS7tf1llJo5NcZ5pxrXF6Z8xUa+x2bshFWsQT3LEItVIMIiDZpRhiiBtM2g\nqlZtN4zCJItajTycKYALAdZQDELb139G/b6KWfC5o+dRxrWMmohTZ62HX1Pr4E9ehquZRsBv4QvR\nYpRRMqy+oYShHlP3P6y2mHou8pWN0YHDpHgNnqKEvUw9xqtzdqfy3EzD5uxoOEc6YhU/xC66kZmk\nLJgVaQRCPYymA0hHAVoXQ4qXZxVlgX+UijyWYuzsQMEKrtBuVJjA04U+i3nGJqDGwnnmQgQezzem\n6tw96PUaxej2CCUJvLiaWp6pz59VCPFbDIkS+Df9qQlsz63t97sIbELgcwof3Ks0wseUUKUNWK5v\nDRSveQ9KuNF2fJjA5qrNJwrQ2cRdhdjGEjBakbClFfCTVqtY6xWWQjLgnFDZmxDyxyDcIb+xxnnd\nICzUu8lkzMmQ2PopaQTu0yeJd7AXlYvYxA9R9eEpB2H0dZDPe50y2vkBYE6m3wLGoj/ALpTsxyMI\n7Ed3SviFAGbAgouhgIA9mT3PY+SWjZNul7nEGZsQw89MouvsFikuSq/3I0Ef4L16Fi4GeM4C9PrK\nchMaQzKL0JPP4HA+hFFf6dQZsminEpCQrfNMxdbBn78wC+SdWYsrEuUup0KKa2MBN8WPmb3xdsMv\n6DeN4iVrdLFEUMHl6Oowel9D4dm5x7JIzdKuf7Sx2NlwYuaCd50xhn3pxs1EKVmZAyihpZ1Z2MLv\noR6hhGqepXvxj1BxqlFCVkECXInOHg9VJcKcj94JdV1xSriwF8VrE/4KW7MrlrMDGliOKIfj9Yk+\nuh1ojFOEssg/wGwoLUiv4ZBiFgO0JSWr7BaK8bie0UcFgWsJvK2O6WDsL6Jkg15PAVDnxLJp563D\n/FQZpLzLzRICJ/TF7waWNJNZF789rvYfQfH46Ma9uaUp3lbTyAlRMkZXaOc6+C4ddL6NcZ1hS18N\n1Co9qGfU/PCro+I9I/BkAePmPPPO308KvTft4hG2tAJ+0moVa/3CLgC7av8fDPAlSObWqSiQ7BIA\nKC7jxhevt5VapnELAtwlT4sbwuuhsrWzRokQLXI8gN9h1DZr1FLwF7pBlaZgHEoBHox1P4ziwp4Z\nbHdnAqsRYlldoXCAOeVSYhRvSE/LkU7ttSTAaGesiDs15hIo4XfYIjMNmy9OoUg3SOIE7oLQUZj3\n52KA0wAu7YPfP1qJzvpCHK1Hzdf98EuoGsFMDerYBSs4AwN9b3gtrmAp4ixDjOvgzxVQDPC01z6b\nq13/LMt+35ImaqxGG2NoKz3UaEj4jHsvStmPcu23K+gOFTrs5APo9sIlCOypzimheE2jBPgkjoxV\nIsxOWMVKhDkJo5xzrqSGCaKEZxsIMIYyzkZ/rkKnCIH+PvreZxmLpcZ1Z0sfuMehhMA5lMXe2Z9U\n/W+m2g9QQsmOQRClePzyYs4KEYp3LdekESPwaDPbPoJAuB9+MZvNALzdOHZ6Dh3S6vk6m5IFGFfj\ndCvlYy4HhUVj+8MpRaoXUTxjuncsRuHv0wtCl6lj9fvWQPWRSGCnJIrzfWSQYgC/S0kKWa3ySP/P\nhS2tgJ+0WsX+vwglDPat/uKZdd20LQzJzlkfucNxRRA8lIN5ScCLwwoB3OYvvLQRABYjT703SqHf\nOWoim0YH71GLY3BlYBkOP+x0ePiwGs/dgOIV+MuxCBTQ7/UU3ESKgrMwMhn5lTH3J8/HuMQS9MgM\nwEx2QAOLkYzugqmJKMqd8OjvMjFzd2QzCIMAX4WqE6j6v8XyQCwFWH4XTnvxeYxML0M338n8dQxn\ntRtvlQQ4RbW9Ld1ekxAV/kjtn2m0l6HdyHIWpE9p4IIoXihb2ZlnaAHnqgUypsZoEYEB6vdKSsHa\noNoXohhUr9Jr5H2vtVdN8ey8QGDMYqyV+gzb60WVSQlNm3rsqfqppyzOvt5hisfPDK2utPxG7bcw\nxYvVmXbAdYaKdoMSVja9SEECa+Q9JrAvvQaJ8xERoRilHnLRAtv+DwHej5NYpSUyFyEVuR3nHE+g\nq3bsIss4mAZLgoL524HKOKGdZDVBoJOhS2dKOP48ZgHoJ1HCo9cQXlgBhTR0FsWgW0BV5w9gb4Df\nBJBmDer5LA71ewd/as64tYtV2NIK+EmrVez/i1C8U/pEmt4UPy2Bm2YhBkmJnwPBbEUgYPIKgAdD\nCiNfCIWvUS13AHg3BBD/GCRLywkhhiBUDn8V38/uAJYB2LbJZ9YigFpcjVrMQy0G+R1GKRQcZjYj\nyScEt+aEXpBqWC24owgcDWHuds2ja2PhC9vh85nFSGohvUxkT7zzFIXzRgvZsA/AkRDjKqAWi1Mo\nHrIxlgU3Qcl2W4+C2/EF9l6BKxnwQkEatGvbg4IX+Y4SatLDJKOYNbgcAsjNCFyo/Z6gGA+H0eIx\noRhCMy0Loyql5Dp2P7q9OmkCP2r7SyheBueaSbvHbF6Oe2kC4hP0Z7yuoRjUOekcKEDmBcYzEjeu\nOaPGYSIFT3cWJUzXn/51Dn9S7W9Er5evgVgzGa8U48I02KJKtw2YJeC8kBJaqyMwjgVkq1GjGnga\nh3MfvMkReCH5DbZ0Cp/XU80Xamx0PeK0G6VpNWYDCPSh1JL8jtn3JEP5SNPJcbtRwooObi9EII/H\n33UdJi/fN9CiAVUI8QcMdp7HpNLxOzaBVqJd8gpbWgE/abWKtT1hJcDHIcDzBbBSGVjOsri352KD\n19WLmoJ4mUZDPE76YREIBssBeEYh5VJ8+HcYgIDVbwJ4EjzFnNeYbAlgKZpTV60WlajF06jFp6j1\nn4AoWVvmghgmsMaJE7U+bWnUUTXxh37CpuFi75qegeDZTHJSApycp7+LmQVshyiGt1mbMUngJXV8\nX0qB19stiyIfxAmGh4oUvQq+/sMIvEVgMsWr6NAVHKh0u5ZWslFXGzW0UzY8bxx3Mb0GUtw45jTb\ndRr3Zi7FCD7FXAgJTDLOD7GAbLgCxmkty3Pi8DU1UMLFG1OMk2EUY3UAJaxkGxsS+EG1XURhz3cM\nhjjFOFsjWYKqj7F0s/Efaez/B72JFtcSOIjiIbJ5G6sI/JzjXrkMYEqodZI2XpfRH7CepngdnY+r\nKN34qjCBCardSoon07w/05o5WiUwPP9VCPEunBanzOvtYb2/RtjSCvhJq1Ws7Qkfg7sAbhjgDnnP\nUq5wY3tS7a2EhO+GwV76xAzjBQF6CDUL0KGMwB2U8NN3BHazHNUF4MPFSP5cg/oXqhHsTm/h3Y0g\nRYkLMiZdUoueqMVnqMWTqEUFJT3eyitDBRY2BqOOBfAfrY5QPCJ6n06JGE7CKLOuI9U9q4EUVda5\nyyIAL9NaPhjg1xC81PEUHI/pjcpYfiOBXy163mgsKkyghLvjfQdYHYOk/jeJS4niGXqA2a/vu5k1\nrDalcPk8zRwkofSG5qIErjGOGUkv7mi2cczZtHuZFqhnQU+xd4Uw1fllBG6jFDb+jAV6UynhosmU\nhX4aVVFgY7/pTamnAPs3p4DKiyhhSoczK0wxSIbQXpR6pdZ+RwpW61tKFuEaJxGlGHj7EljXss9G\naplmlhB1Cg1cHCWzzkaRYW7JHDodSC+OSX8+crW7lGJM/US7J/PPZo5UQL1HjU2VIhYfg5v+zXZj\n6q8UtrQCftJqFWt74q4qrxbT2rxnCSDSfMGNeDtrfeYKm0F1XJM1z2Yh6V91Wkovi4HM98VIpACy\nDDEOwEzGUJZSE+neEH6aeQBsjO1rAXwE4BcQ1m8H8xAgcOiLAzGu8lIsQi1qUYsAgUvUopSieBhc\n5KKUQqgmy3aY+Gv5qQgcrsbJYXCOEAJYHojptnk9AjGIe0C8VEFIuHUKGhnMOQxuGo7wIPxwxXUY\nGxuDm/gBdsu3CM2x6NmFwn3lymBKoYjvYQ/ei5O/ggKkW87tq56H1ymlN/TQ3+X08nFdSPG4BOmm\nXTgsR/sL1XPTQDHgq41jdlH3N0PxwqyiQU7JbF02vc/71L7r6c0Cm9/U++2j/0d0G7YNBNbR9gcI\n/Ej3wh2ilphBMZ5Md2Gd2ncB4SG++n1N6L4mRD0buQDYYQI3EbiBEqbuTOE2y/ccZ1hAgWX1vBUC\nANe332hPiiDlHb6XYsSfQmCTAnQIUMo/HTAAM09W729Yvd/v4q/z/reLCFtaAT9ptYq1PeGfxrsa\nRQGFUCkp654JwDjqJHiJOuOQjMKY9lsQoDWjLo8O5uSeZGMNQQDgJsVI6P2wA+r5FbYmAS4HQqWS\nTj3W0nolpHhyQhuX967ElQECT7+2EaI9xoCPbo4YJXSwH708Q69YdN6esuiG+RcXCjb6HULBvfyd\nkh0XEaCtJ5yWgSvsy1KAW0D4u7R0ab5oWVvikpiQZiVCfBTH5FosPvbRsxMFePsd3R6TKA1KA+2c\nHpSwk2MMhKiwaRSP4VJL/1PUOJjW5I+2PlRbHSiFsHej15thpqjH6cN9RME1vU/xPFzPbLHma+k1\nqJrphXD1V0XvYt5A4GjjuN6UtPgoxeu7m7HfpKGg0reY4n3SxzJGRf+wBvTvSmAwDQO2gPMGEfgX\ngfMJbEUxcP1wTc784XhU/yBwqeV6TSNsEYGBBegSoLckjJ8OjcY9xUtmO+5JShKF4yn0qWzg6v8Z\nZsP94etxyShIZvfBaDem/hvCllbAT1qtYm1PeIgyetLKaPgNPsVpXWeJa9386r/FOKoU4IcQj0dc\nGVE7A+wIqQm3GBIuyhu2oABMf1CT4TwKQ7uJzYkSOFs7a6NSxF00DNUI8jtswRDA7YDU5oKDsYDc\nuQcMtzjA6Ms4cOSd2yGz9gXgJ31di+ft9C7OK3yupZTi8chTt+2vEUr45v1rcCmLPOtsJlJgK8+Y\nc3zAaGstLPZbNKIEbs2j41qULMoGtWh8RZ9wBO3FY8Nq38W0ewbqaSc2nGXrI+9o2EN58fxnutrY\niF7v1VnN0cdot4R2gsaDmtjOEOOdT1HCh7vQ60VJcA3QIlCMa4d8t57WsL71vF2VrkmKgbSUYshe\noJ4JDw+CsUXUPX2B2WzBheq8zykfUAPYBBwYhXNM9+I5HuOQ6uNcCgXGbc51+jyjqyjJLebX0NIc\nfY+wPAN1luM6E9ifklDSg5L0MYQtUPj7f1DY0gr4SatVrG0KtwN4BcBz8htTLEO2jMgoCvZjBeVr\n38LNwzuVoZZUhpuVXDBnj7Ig/En313s95ctTz9ZaRBc2g4H18evsCnVIBcLcHp8yggCHAfwHkAxm\nuXI6UPBYHxK4Yz3MG+4xqIpi8UMPrlq66engr509BkItvYv69KZe639D1EIQeR9DtVRwshQxdsEK\n3+rzRitblyGWdG5JKeIuxnRAvIHaD2lmC79+xgK8DQMwc/CheO6i9TH32SKkngJ4NCwZnhRCSXPs\nY2qfDevnGAMz6P0o8MuYK6Zk6B1NS4iWQs5oejMabG3lHFXBKz2n9D62qefnaNfkwUoTuLmA8wIU\nnqdZFI/aBNVOigLY7ksh5LRl+q0Wk7p6Tm2YQ18OMO3cb4zzkgRu1PZP9nku9OPHqmN7U0K1q0Vo\nScnUm6ae1RiF7LVcta3Xb6yhGJJjKCSypm6zKdQJZog1F5brDp/rLNOO6UcxPOvVe+pAI8LqmWwn\n9Fw9YUsr4CetVrG2KmpiPJzyZWJ5cVgBKWicUsbR7SFU9aSkyPtktnFduAHvhHirmpSVREl9tjH+\n7k35mrqHEi7x6HEGJtSchTt+2xdvJi/G9ckgKngEkNwfSEWyWTTFFA+Is+DEIqj4ugSJOQ63VkX5\nInY/ZpvMXsciVVfumZQaKHxB3zBbxiZIIC+4vyVETdQJApyAM1iOKIuQ4vb4LPUiRgwttJ0PsNvX\nx+IRHoXH+QBOcBlnFQjzH3i00VOjFohBlEy7TWgwZVu0vB7uwt2E4LiutFxPXzXx656du9W+e5g7\nxLMPhWjxB4rhYDPYSgl8oO6pQydwN7XMMAro+jdmcUphAmcWOpaULLQGiqHzMfNkHjZVKIZRmAAb\n0IHHYxL74ZdMNyz7HOCGOc4bTW923P7UvIUUI9CWeJCiRm7aDJ1H0F5Wpk8B5/5q0edBbf/19Bok\n+pYhsEdzdc+hVxElOcUPC9hR6R5Wz23M8vx+SQkF6p7XJIEPfdqsohBz2q6xu3bce/QvbxOiUdap\nXZosbGkF/KTVKtYWhZI2HGI24+UtetKIeaeqdE+ALEEidhdGx5lNUz7C0vIQCOGj/m7WwZWlxQpI\nJp6vS5kCVjYnvxCBrQq8vmICuyaB4QOAyb2BmXMUG7XaP5hegy20AL2eGo270v07vc2i0zZh9f7/\n4BVF/0oYiPo0gStVO2VqETiWlkyj1iI0wlMZCECd4jkqGEtB8Xo0ehBew36xHlhc1x1LeQIeZAQV\nuvF7AIGD1fEOsaXKbmQpwM0BbizPAbeDvXwRlZFlM3o2pWSgfUsJmzhe1B4UPIyNqmBBgdd5nOX5\nyLAxq7XxuM6UVPkJtBZq9m3fJCh1Ct1exzUUFqZg0xIZgLtiKsvV7Q8gnYbU3bQSX9Ig71XbN5Ss\nubup2LxpVE3gmjGoBtGeZXdwAefeQq/38QBtfxcKdMDJWDS50JIE/t1c3ZsrFK+7ec02hnrTgJ1O\nywclxbs/nXZD6Q+6kzdsRqj+TF7+3x2N/zlhSyvgJ61WsbYoRLZmTAbgfPQOzcDAE7T96/bDL3Hz\nHRuJ5/QfItRYg9WZVWqyzmjNL0djHT5eBfF2JSD8Vb5f5ZQvshDFsApS3OVNjetfCeFuMRmIN7Ms\nmEECr93WZwcGLlib2H48gQwrEc5cj4tjzGZ7fbE6i0ZLCIXIcQmzmIoUJcTUpJRpiufmTWbLknxM\nCWHMovvruZ7ilTLDN6HRmNgP2UzCMMD3AB4LL35N347VruN2SvjGldln6NmBkg31jbqvTkhjaIHX\nebllUSPFc9AsBm6j/Yto96JFKJ6x1cavUDxUS5ajq62iQT3AA33O+8Sil05KupgCGu+k/q2Dqp/Q\nWioBeDrAiQD/CVeCQ2Nf/SiZdZ9SMmbXo5fyg8yROKC1VUoh2qyjhLFOUb/3Us/CnpQQ3DgKoN6G\nqfIklfzVQvG056NTsG1RWjx39C/LM5sGfxkFr+VX7iLCJmLu2sUjbGkF/KTVKtYWhcr7swQ9OBg/\nsAIRFiGVglAFBAhM2wvvZHTQcRliPB/j9Beunq4UcZaqybNeGU0pgLMBbq72HwR3BmAa4Dt59NyL\nkn58SDMWmTMAzLlJiowOosIOUJiKzWLAMQLfnHwgxpeP6Uhs9JprdyniM2kvqNxsofDVvE1hod51\nTbSZp79eFGPkcQrz+doUIG/BnjWKkWSCqA+mFKz9WO2bSRnzHekN39SvhcXvwM2uH4Hg7szs0MYt\ngHR0Z3y0FeVDwDFEQup6+vjdE0q4ZQ9K9lRfY9+2lIyw0+kt3GsDBlO9NxYWcu4C8BKAxwPMCVqm\ngO9tJUt0z8pGhd6TPH1tU4+aFSVe260BoJWDi2J46GzzNv1OUsf2Vs/TRxRMoQKlMwApxu7c0xDA\np41+1qZ45dJauw20e1bmejUt6Pq3ZxbcHjQ2J7ymG8t3878MxqZkkObKLMxlUHmiBJTwoHlsmnYc\nYCeKl9pmVMVo0MC0S5OFLa2An7RaxdqiULwsqb3xFkvdkbVQMZJHEkjPxAB2xkp2QAM7oIF98RuX\no6s5sXZR7Q0bhjc+K0FC92qFAe6t9XqHZV7wBVWuphwFYP53wIvMZtbMo2BvfqLbm5JOA492GItr\nUIvfN+9zz/dm9hrAL9aUYpQw4UOGDmE21tz664ViYDiMzREWiP2h1HIzF9nvfY7tTW8oI1qM5BzL\nc/A8JEEiJmFmdxcd0JA+Hf++g3YgdITi1di5Cdc/ktki0hGKt6KDtv9tSz8ZCvVBL/W3nkB8Ik5N\nVyKcUTUHQ5BKAbkKKT9Hf4yXYyjmrCvZFCFQsRYWPx9AOgIxTuNA5ic08otZz9mB4sX5N72ZYhHm\nqBOoWtgc3hBuFGDjok7B2BViSESpQuzqvG0JvELB/7gwPpQPp1sI3Ewx/mfnaVvH4TmlipqcRLO6\nQgkxL6M/nsnvOfEYxWpczGMb6AMwp3gyt7TcizoKb1+7NF/Y0gr4SatVrC0K5at+elcPCwEJcBwV\nPcES9OBjOIZP4u/Rpeg+QU2mThbIIaqtiwiE++J3W1t3a73e4zM3eAp8rqYMA7DkEeGU0cN6ScqX\ntGuBiBajYdPT8RFq8SVq0QvgRhAvm8P4HgbY9PI0FlGT1zs+E+cza6KPHL33Azh8J3zsSoUPoYov\n48DYjvjkn/nuBYUs0dRblYVhbwiGTgcvn0p3eZATAD4Hr4fqUnVG11tw/okVxtxehRAn4fg7aCc8\n1BeAgvBHlHR400g4Xdt/I93GYIaSIdiRyD7oGcDGOh8EeIhPv+W0c2Q5z0OMEqZco9lVIVRtMR5n\nhUfiucRYXBdfjq4vFdoHpbSK7rGqp0YQajm+5hTcc2wxki6PYwniMYCbasedYlnEbUbsXcyy3G9B\nL2De8ZZtrfY54egQc5f8IcUQt9UELIgjT73Pp1EMt18pXrpm8TtRPvYKJQKNUBIiVqln5i2qq0Vb\nxwAAIABJREFUUDQlgcC8povy9N2VXsxqkECTKhS0i0fY0gr4SatVrK0KgUAxEtOAjI65DgM8jVK7\ny3HBBylhqSIKhmVrKuwUNb6bQfjRfO8TELf/DQD3h4T8UsYxKfjW9GvUcwsK6DuPB4IBADsCWLah\nkDE+ZZmIlukTx9IqcMeTkFr3XHyIWh1PxH6QWoLjUQBnVqFC+YL2Mwr+QoOKpyjDpS6AdPQWXBAl\nwGXoxvXxKzugnmoBXAgw12LpcP3oC9o5AK+BeCDqAa4AuJV2znqU0K0KLbIHwFmQsFMI4PvQvCUE\ntnkGh0erEGJHrGIVQjwDd6bU2K2i/1d8kAWGyiz3IEXgX9r+KgqWKKTa/YECQN9I7z+OUguvF0MA\nT7T0WUwx6M0TIhQj6huKVygvJ1xThUJ3oLv9QjRIPnOcW0rJkPue4rnbNMexuxCoD6Gqvjfm06kZ\nWYIEN8SczAL02lI7di0K/YozHmEKFi+k/f9lukHUNmLWWWrfa8a+DN3kr+YWIzCV3rB0A4HNCxwb\nWy3Hd9iMsCHFc2k+2yk1Ro6R6GQCmh7OGIG3VTsBitGve97qmL9g9u3a2IcoCR/tXFSrJ2xpBfyk\n1SrWluVenHxOR9SlOqA+XYp4DMhMhQpXUKgLjqIvrQLQF7/vuzM+zGyJb3gG7mQlQixCkgGkkhAc\nlZMGH4bwXv2IbK24MMDxFKPMGn6gACzDzJLhjbccNQzgMuDHNNA1uR02uVhNpOZXWpqySJ5KIPxT\nD8Q2OAeZUw7A3CuHWgulBijZY0619we4mvgpijFqq4EWZRMqyTex1+4wqCwqEOEf6MNTcLcZ8k0C\nzGnYUYztryhlS84sRnJXeMM7f+TRqRTizTLY2BvH/Y252CD8Eg7il9gmwizdxcZqwZpjWciiBAry\ndqrFS/dAhWnUyKN8QAyiUAQ4GYS9zXu3MX4y+LgyYYD9LX1uS3vI8iOuwaLBPtdrGpBpAles4T6K\nqQHK52E97o4pXBsLuDfe4p9YJ0iDZ4vCx/QEJYR6rmrjJIrhdMqGmNMd4D8gSQvdKCFI06D6nRLC\nNnGRztj+xCxb+lvMloqaSmAo3fihNAVoX6in0+ZtTLAZIVsCX1vamqv2+RWj1re4OnZt2mtHTsr1\nnKn3biSBayjlb9qZ1Fdf2NIK+EmrVaytCoWPJ7wCXfgGhnEKdo9EUX5aE1rYBhqQuBpBnodbeDlq\n452x4ilI6EN/r5MQxvTLAE4KID0qjcD1amFMqclOx7F0ohcsGSYwWNNhQ9FhHiWK+Vi6H36JWSbd\nCAUI3A8Ajh+Bs6r+hYZjRmKC38RB4Hh6wws3NHe8VZvllNCAswI7X51/W5128/TqobIoQSL0IXaJ\nDMV7pseQAL9qYvunwgsoz0CRwTZLY1lYT6R4Rg5Xk32NvtBRsqMSarGMEzi+Ce13oGSXBSnhv8Mo\nHxA9Czi3cRE9H+NYhZDyUmVYjQbuiqlWzw/Fu1dveS77acf0onxEnMXCuJdq6OPRonjZLqOULPmN\nbs9YiHnKxBBYl8DDFK/UaczhraBQZMywvHc0+iyI9Vy12gfgEjWPBAEuuxNnDqfbQ+rc/3rtOdDf\n12PVs9PNeXYohnI5vSz1pNAKDChYQ7tBRYqxlod3zdPWzfTOd3ECR+YZV2dbptqpoT10GGUzvWft\n0mxhSyvgJ61WsbYqlDpP5ks3zefowRCSzw8g4aMAJDPLdXof/JEgsCPAo+BNg08C1NmBj6LbYIkS\neFjb349A6Hf05Ss4gN9iCCmuaw2IyWOAhUGZG4UYuAQJBlGtd5yhcOZISK8Wp6IWi1HrTO4sAngp\nwBliTHAP1f8LlvExikE3a9x7EXiVYli9xAIW8dXssSO8xm34H3h0/Y0x/U7lUXF+jwC8JX+brvaH\nwuuhWrjGtJcF4n1mDe/xlFI6P9JNqtksjwsl9PSzaiNOSRhwMDvFlOoAV1GyGQMUQ2PxPKyXNPFT\nFYhwKN63Fq2lGHGLtMUuTvGeFKv9G1Cy3qJqq6dPzTil1+PMhn/eIlCp7S+hm7g2oq7PoSG5PdfC\nqsZkOd3hOOvHBIGdmRsL5XiX723aYs7H1JzhNJUC+DSlBNXrlGw2D3M4xSj6jRomzkfvm+gNsf2q\n7d+SQo45jWKY2rzYY+hv7KQIjFTHbU+pqZkrXFpOe/bnRxSPbC6jKkFV5JuC4/JLeohRSvHkDP+1\nyxoTtrQCftJqFWurQvn6NF/SL4xjNnsFB4wpRjKiYa1CkBTxW+FmtSbA2erMPsYiHgcyn1NwKAHV\n9iTLC79c67tsMg6p17E0o3FXgi7G4e8OBrZIC22QNFGKeCaJYn2iDBE4PFiKvbY+Ba+UXI5fUAst\nJMOr4fawhAFuRQHDumI5BN5dw3chAAlnPAbwWviQLa6Bfv6m7kdIbYqEkiUAn0SWG+wV5Mj+8pN9\n8eaHFYiwE1axGsHkQMxoMuM0xXNwCcUQeJ3AYIDHbYFvFx6C59M/YpB+P++kN3SatC16BfT7mrEA\nhSghj4Da5wCdQwTGOboehJf2r0RYB9ezDLEowG0sffSkGG2O97SewqWls1Y/QSP7lMDLPjqPoduI\niRC4Q9u/C73hxTjFGMnLyM5sMoF+vrXmIyU8Z77HGYoxdzOFHmTrQu6F0fIHFpvgU63ffWlnVR/P\nAjy+lPp55vy3mNladrr3KkTgNksbAdqJOfVxmKTOb1BjelIOnV60tDGFEupewKzR7xDXJilErNuq\n84uYO4PUMY6X0+Ckape/RNjSCvhJq1WsrQqz5JbOpBEhsK+2/0QC4StwZbzYi+tcAnCgWqQdoyoM\n8B9aD9sBnA5wZU8s+mwputerl30FgZ0orNumazpNYLg6v7gIqYi+uxjJKMAdVQcVAD4ADv8DSAch\nOKHwIPz4LwLz1QQWJXDPqnJM3e9opHYfhdSKCjTQlb3Chca1ZQDeSPEkLVYTUES1t5kxhgEqksNm\n3oUbkPXuxAHOhebFa76wM8AnAM4B+BbA9SAM9RsArLQc3wHNzLakYkOfiw34KXbgKnSK0UXwWHA7\nt1LLJrsV50a1VH92QANno79zkz6k12DIUAytIT7td6d4ZWdRjJme6ncz448UPqLt6MUexdlIZssO\nQGaFcepKNJLYuvr+D71G2xHGMbZSIdY6ixTAsHnsNG3/XrSHF/OGEdX5p9OnVqLl2Bss7/HvtPAe\nNU14EbwfOo3M3RTuM5tnLK1+P59ioK9S7+54uksHmYWfTcPMnPTqKfxqF1MyFPVs1vNp4XKagYF8\nGQcmZ2Ejs23rO06ZF82kj73VvmKKd7QDZd7pQzFWz6QYlwFKAkEhmYIpAq+t3v1plwKELa2An7Ra\nxdqyUEqw3EsJc+yq/V7uTBBX4zLaDSoAAip+BOBkgAcZbTueqC70Ln51FIPF9jV1v2qhC7IAdmdr\nAHgUBCT8EoCngStKAR66Ez6+9SGMGk/gGEqdvcEE+r6/Pi7YbDTS/zwQTBQ1NjRL03SeZc6JATyV\ngr04RS0w6xrXV03BJDiA1yfYJA8Ji+EOaRBioFpK+jRFGICELmOqzRTARQBrlN47UfAuKyhhzdXK\nKqPdQ7FI219J4FlmGe/P8mnH9YyskyXzJ0AWIcVLcQ0pRvI42sH9DiZtJ6NtpxyHEyJKULinytTv\nZjv3UepGmh6QMAVIfQCBWV9g2yVdsbxeeW9/A7ilz7WtsPQxzjjmdLoNuBjFGFhM4VbSjYE76Q53\npQi8oPYFKB6xhXSHF79mgSE3irFiErje5XPsumqcHK9whIpSZfWExQDvA5gMIJ3eGR99E0LVsdQS\nZCgGhZP5ZjMawgQ4EwO4Nb5KVyIcATgFYB91/s6UkJotnGb+FlLtJdXf6VRGFSUsPU8/fhzOYyXC\n7Ig6ViLMiRitP0Pr5Rj7HSiG//PMwezPbMJMROl2r/r9Tfp7zPTNyh/XLmtU2NIK+EmrVex/UdSE\nHCXAOdiQHdDAQBZuoEJ+jUf3BXgywOMAdqSwcDvp7Z9ReFE8jNmUL8Tvjd+1CvEMwOs9igDxTQFM\ngqQJO+znJzDrDg9RWLtLUIttOl6C+pt3cnNDEAhq+h8HO0u3QUzqGaOJ9GaKjWnCKJchy3VFgCxF\nLH4NLv2AUji3meBRrgNvgep6gH+jt+h0jMD7zetH9Sb150wsi+4tecAyTgdY2nF5VHpjvqvJAFK8\nCDc6uKMOlIzJ73wWj/eNtgfRa9Q3qDY+t5z/H4rncRXdC+tyikGqe2/CaQRuzzNG3xrthAmMNo4J\nqLEMqWtKGsdfpx3bhWIQOizgiyg8Rvuo/zslYj6heIteZoGs15Sw0XPMGg8pAg8q3Z6jeER0o6Yv\n5f12UvvruQYLPcdRenMSxSHKfBKnAMEfouLConCDXWO5vxl58GvYHUupkfUmIZ5bJ3NzJ59nyNw8\nZZQInKyNQ7Uaa/6BPqw0Dq9AhEvQg0r/ZidsqL560OsRS1DqW+7K3EWgnffeaiC3yxoVtrQCftJq\nFftfFDWpzncmpR8wmAfg5VQlwl9AsrrUYs8hEK9RGGCoFPFFy9AtYrzktkUvRknvHcosY3Wckh7c\nS9Nkc0h4MQLxuJwA4GZIKKSD0jVAb3giePIBuBG1WHbiQbiaXoLPD4wr3h9Zj46zZZADoE3hJjIn\nqlebONKvqWtjAGl2RB0XYm1nsh6X59wjAH4K8EOAw7Tfu8Pr2QsC3JUSxrWl0BdIB8EjAP4JcAWQ\nuTeMyvvUvUwz6x1yEQJSsB/mOE0kcDUFWD6FwFbMfnGTAG/CGFY1qprJFCMZux8njaaR0k4B+Jvt\nf6kfMw2bD/oem0UWoae5IG5GMZ7M83+jeGnNmn4RdbwHe5Nz1MRbupJieATVNZcax5RTPF9HUADn\npk5zjeMrKR8rB1EyYntb7m1S6RylANfz0jNQsspsXGl6zb6HtOOnWo6dmq+fQoR2wklS5ovFarzq\nLfom1FjzA+zGTkZ5wEqEM59ju+cphnlfnz5M48wEsCcIXGzoW0Tglrex98+VCLnwdTWo45fYZjl9\nQtIFjEWAEm5cqp4lG7/WnYTxJeLWV/93PduJO/9qYUsr4CetVrG2J6wB2FjUWE1KN1BCDuXqtypK\n3brf1eQVpMWrAPBjaMD0IqRSF+Bm80VPM7tYNtDw5FB4fi6n1OyzZLyxBAJyr4Qw/k4H0E07v1Sf\n7DIAr90V8Q5jsRK12EodcwWztbt+ostoa2xppjEHRQH6epwoAFIdrxAjcKtxzJ6UbL56ipegs7av\n8g/0OXoIvp1Sg/qlO+KTlAa8dhYwH4A4j4QXX7Kntv9xbX8U4NcASygUBDawcgHeMO6m91mMZHw0\nJpqg/bn0hkZNL2Sc4rnU2beDFB6ixkk/A3AiTuWO+DizMabPhEYWarR/KN3egxABjf6Dg4DM0kqE\nU+WI8hJc5xhGU9UCOJR2g/9xSkjXXJhsmVi/UrxGvuzjFONgGAUwXmzsq6YY6A1qi9GLhfkh592R\ntk1PsL5F6JMJySy/1wxKoeJ8OJwEFecXZXE39zfk0rVQoXhU/XBONiZ051n60rmn32BLVhuPfDmi\nXIi1o1SeTErmmx8BqG7EmX35kA2zOzyZr5lgZ6xsdlUICj9XPmb5L2kPX8YonljT8JzXXH3apSBh\nSyvgJ61WsbYjLAb4ECSbKw7w/UXo6XhvHO/CF8wCWp3FrZ6Ah/lZtempy3YknvSAOQGAEl45moAV\nZ2JpuwgCou4D8YidBOA3NAJreaDqf/ExeHRxDGXJeDF4wghwyKlI37aDmyiT8kXfnb7GA/dQBkNU\nTYZzkAOoTfmyXaTGp4FSFFg3mAYYE2CMwDtqX0cKONop1OrgIEiAf2IdHomnMsVIfg7JQjQ8SPzC\nMp9O1vYXAzwDksF3BVQ5GArdwA+qP+eeX5DjGrWx4jizz55YaCrhqc1Iwak4YawwxftjGnU29md9\n4cxJlEgJ+c5VbV9A+ZovIrBuMZJzoRn95YimJuCMSdSMVQpg2VwwY5QQl8m+bfNmNDCLEdsvl64+\n+l9Cb6mbJL0G+4E52tiC+RfcNyzn9aSbgT5uGQtzi1N91FBCj+b+35s6Bj7XVEwxVm36OCF+/bc6\nygfirc5vGYDD8Xqjt7MaQf4T9+nPXSfV18aUrEQb+arNSInQXktvXQIbVyK8P5AOFSEVK0IqVITU\nnt4rbNJY2JIWTB1fpddDFaXwiI2h9x1LrI5O7ZJX2NIK+EmrVaztCM+Cy6uRiZ6IB0w3dtBnUo5Q\nauSZbf4bKmSl2gxPwOkzmDUSIrRURC9A104Qr0oEYBS490sI0FmR7nF7o9/IwVX3LNrteGT2Pxqx\nOV1wcDPHaGOAZwM8EZZsLc/REmrZn5JlY4aiRlvGMkVZ6K+gGwORUfsyq9CJPbGIRUjq2ZNPq1Z7\nA9xdjY15mzSGcxYBHAkpOGwCtKsInEPh4Rnuc10DKN6KtJqgd4QQsrrCGP0xyzaxe/AzFKKwsyhf\n2R3p9aTEacexJAg0eSGieIO+SyMQsZSGicq4wAmz7U9JzDDvVT2z2KuU2kL0ejLMxTbMArPpNH3v\ntVz7AsuYhAn0ztHOBGbL5Tg66wvrzZZzjqUP/shnc0q2BChYP1PHFIH9m3rPclzTeupZ1PtIU4D+\nHmoHSlHk5/Tfkyjmv3F63Tm4Pf4EjtK5XpLMAstz8WnZxiNKd1Z0EYGn1e8hAvOjKE/+hnUzMZQ5\nhbWbTapJSexIGzolmf0YaaCElrehGMh1Spcb1Pl/o9tDlWY7MP2vFra0An7SahVrO8LnzTlhIGaY\nk0SQlvRftd1nabMC4LMQoGcM4JVfYesSCg7kTDYTLwDwYTRimt4n0J0d8OD9FENkwtb46knoHFjd\nZhFn90uhFjejdnUKy/IggN8B/BngmWjEihlHyYI9RU1KIQInaPtGUzwlywjElqAHF6CXo2xYLUS2\nIsOLCHzxDA6P13gy3pmClOAIA6xTY6MbN2GAOygNAsVIvlqOaKIM0Uw5oqmBmHFVwSMgIdQFxiLS\ncBFuHAjJFowBTBcjGX8V+9sWmrwEm1QFtbVFzSmebLZVT4NTiOJBvYRCDOvHcu9kFXI9d/IVId7H\n4fSG2TLMfsGHCZyv2upHCVnXUgxNW8aevtXRx1DNMR5H05ss8Brt2bE5C3VTQorHUUKZc5n1oE6j\nYIZKKZ6YORTOryss/SQpnp6w6jNMYAnFC/ssxSA/ll5jKskmJWYUNDbl9GZ0pgnsTsGPOTpGKWH1\nCRa9HAMkxaxBHCJwj9bP/Xnuq+3Z1ImKT2Z+D+F5qzEOG6txSKotSMlEvYiCrdpQO7aGYliZ4fda\nZhN3ftfPaZe/RNjSCvhJq1Ws7QhvgBt4ndoVU+vodgMHfSajJLUsI0vbRTmMjwAl8+QwFsxNw5+l\n268pCS3vczhej6rJgNfgX4kiqRdIrD+FuHAtYrsJy/O3m7PPveDGJYUAWtmWKQBfs8zFzpSFMUyA\nCZRwBF5kOaKsQIQ74pP0n1jnbHW+lSWewDvP4rCkj0FlZu7FAP4HQlmxg6bd7hWIuErKlCLO9zG0\nIEZ2KoZ6Q4E6An+DYEMuBPhsBSIPPoUj0yazKzWCyRx9ON6NyRSAeh+fBa2BWuo4gX8x6yUKUYwO\nz3NHLYX9K2zNTlhFBRKOALwHYIDAWHrDbPMpxq6Ph5Olp+Gus1/BAZGV6FxPbzae8yx4iutSQmvb\n0JJtp8bjZm2x/ECNiflxE2HTSqNUUAysHalA8Gq8Ta6jBdrzHKLCAlKoTQ5Sz3aAktLvYJdswPUg\ngVGF6lfgNazv09dktX9tigHp8M4VwsOUpOBG9WxFW51A04jTzz/R0POeAvr1hFybMRZjCVxKCzGn\nemYOY476qxRy5fVpZBpSDLaHKVQqOcsStUvBwpZWwE9arWJtR9gRQrTZAEmjX3IknhpCYaVeSWFy\n3pbAIcZCk6R8nTa5RIqahJ9TE229mrz3LeDMycDMhMyVL7AYycTFuKFx4VqK7uyBJRlseX8KF65F\nbPhOtB9+OUFdyxIKFqyxBAjFHX8mpdTL7dRA7VqfT1jmwB99rsv8Ek1SFvvGjLHrMJaV2jpQjigr\nEXpIG5fraNQxJBCvRw17YQFL1PpWgkQcwmBulvKpA7i7qVt3LD2moxFRK0eU07Hx5d4rsV5bF3qx\nKWE2eht5L8TYTJcjmvw7ntApKcK04EoKFYoh4Rj4UUoWoEONUUUvBiRIS1FpCsC6cWFdhU6RB3Di\nPQAHasfYDLg/jHZKCYwgMOpT7LAxhN+rAUjXlyBRdzbG78GsZ6KBsvBrFApcB+Der2G/y5ktJxPy\newcovFh6PcsTKcaL4yUqyNNIwfe9QvEoPUKNa4xews8kpbTObRTuo5PpE5qieLlyGQwJ+pTLyaNx\nAFLk/BQYyQcU7KPfR56Df3qXhdW707epRj8bq+fJhEE4hux8pUeCwoMWMM4/0/LemNudTR+bAkcw\ny45fr/6+Q38Pbg91vU4SUn/1/DrXHqbmdW+XZgtbWgE/abWKtS1hOcB9IYBu3zInlBTskyjgzvPZ\nTF4ZCj7FDCesgGCBPoV4WX4HuKv7zHO3AvqkgHsiAIO9MX9+ENWNi2k6AJ62T2Wi9IKu9Yf2qF38\nFvaZqSY855gMJTTTRekxkdmv3IQ6Vl9kivbBWzMD3rnUWiiYXuBnmMA/KR6XDAHuh9c882lHrJpn\ntFNMNzh6BQEuQk+OwiTugqmpYXjjeblXnnp5YRlHt2yFr/tXaUNehCT7YzbTCESZB9yt6XE5s0Dy\nIIHHZAFhXxiesnJE0z9jE6ecxT8LaLuTWnyuotvoXY8qTKoWywYCG2j716Z3Ya0ncJClj/WZTRgI\nUjKcTIzbMfSG2Z7S9pdTDPMggeA1uDRehJTu4U0DnKqOHUzxTuqewsMBhouQaqhEmNfjEtMQdOmT\nY7w2orDRe7xeNvkKW3ecjf6Ll6J7UruuL5gl2l1mjGGUwLkF6mJjlde3eflb8bQaAOgUUw+r7RSj\n3ystfUUoHpl1aPdK5TOwPFmTFPzV/ZSPwDmqjzjFKC2ieBlrfMZmCO3GmLPFKUbu8bR7VTej0B5M\nYDOgElQcWNoWInCM5bha9UwEKdQTm1C8db51Ddul2cKWVsBPWq1i7eIvlOwSFzYmjUAGyPwMN0t4\nUBZrAOI9+nkPlD/xCg748nUM/yiI6sZQWqgUHPF3pLY4FSuWmex57q2OkkpeRntK9DJK2KkngbN/\nwOBINYKNBKaliCcBWjO2KCD0MLO8S99QFuDN1USWuQA3s1xb/0uQYB/87izAnSiLcCej3cO0STxE\n4fBSBheHK6OqARK6+rvfuD+CY1/tiUUsRpJb4DvOw3rOAuMBJee4d7tTsDIHOAvALbjgpGoEXVG+\nGtTxEEx+FODeAHMaCcySZeqL3jFq32RjYUzQjXEpomSU6ccEqWo7Ujx8p1PCIduq/+9JIW4sMXTo\nRWFPdzwbaUo5m47acS5MzAl40PaYmR6tEgK9j8RTneFKmiArEeYMDNSNt5z4FWbrxC2gGDIXMg+o\n+UzcuU0f/JGoQohliPE83Opg96LMEmGeTjd+bSkL/GCiGBa5SDCtpXLytLozvMW749BqSlIqFjjk\noY7eM9V4X0w7pcEHzE2F8IQ2HgsoxsVVzBqeRRRPX0GFhClFtM2PxxSlll+QbuzW1ca5WzGbbe1g\n+W6gVt6mgP7N8HCG4q1/hBLmKyIwnO6PiAyB2RTPvjk+f+TvtV3yCFtaAT9ptYq1ZaFgOn6ieEZe\npzUUttrt60ZPehm6zYSRLQYJQR4BCXd8vrPoYuI8Tv2tE2ZuMRqJPY/DrGApHs4xWTqL7S4UHIkf\nrsLxhEwlwJ+wKU/GvTwWj/ANDLN8oTEAITZ9Zl38dt9cbHCumkj/RsGplFClX69E5582xU+ZDqhn\nDeq5NhYmNsP361LVvmOWk2uEMWZbUVL/R9HjxWANwEEAc5aLUZPnCgPflCHgS1Tq01IxhLZhehVC\n30zB7tFeWMBs5lyaRUixGsG0MvR+gcZxZtHrPss9SFDA0bav+7eM8/tSuHZiFOD/jhRD9iECqT/Q\nJ3MWxmeOwhOpMzDhRsuYPMJsRqETRnOer8kUI6aGEv6aS83L8QBO0IhGGxf9Z7X2d1VtRn5Bv7Cq\nO9l4fCes4hsYpl+bx7Nm6HuCsfiZzNzlFMNxMyq8zBB8G9LLRFUjyJdwkOMdWUs79yAKXmYcrZxs\nvjpVU4DfSXUPnGLPzhj6VhbI0epI9f436h1AOg5wLddR8rHyvRrjr5glHq63vN8RdS9H0Bvi1I85\nld555kIK6ewMCtP89gWOzVB6sV5Biufa/PCLUDOOKZx2pkctRZmbLbU3rf378YfFKJjCKLMEvLax\nMPv+mc1OKmoXJWxpBfyk1SrWtoQBgH8HeN/aWHhjPWr07Jk4JTQwTE0026yRHqWtuHqxf52BgQMt\nBlUQWDIMUk5mUlqwMy5j4M1+eAG1+AO1GItaBChhPHNycBblBAUXdi/FAzXVZ7Jxtjp6a6NZiofy\nLmSB67ESJH4NoWo+s6GlL5wJkEBRHTqe8TSO+M+/cfrD1+DS7pQvbXNyDXMNG7Kq/3PpXZA3y3+m\nq5XbtOtlFUJ8E/twa3zFagTZCSsbsV7qNsUBTsyh0wf6tSdRzEtwPTfCLG6Pz/gpdjDH5QJ1XikF\neDyGrrAaQDGmEovQk92wjMUq6luJcAbgqdpxZq0826KyEaVMjCfTNY1AfCSe/1M9uzEInsoJKVdT\nW7hjKKOZWFCJkOMpdLbH8ty/9y06Oh7O3pRF0jHK3yXQuYORDBdAmpfhqhSBZ3P11VShGKcBysfD\nnRRDecf8Z1pbW88pgi06p9gXv2eSKLYQCcPxRNrIRPXn/Cbt+Cqfdz9MMZjM35cY72hOHjTV/smU\nUNrnzGLlwhTvrsdLT4NMl3a2fqfvgrBM6pn4mf58bk3dMqr/ZmDi2kUJW1oBP2m1irUDIvgOAAAg\nAElEQVQt4XVQWJwipBIbYVY6ggrbS+SEs07L32YBvUrYTSPV5PlqoU4CjADJb4GKyZCCxyWUL7NG\nvV4eCNaMRRS1OExrcxCzbnJngrxDnasXwY2p43IZVFEKZsJJoV9GDb+jeiyHUcy4EuHkixiRNtrx\npQ0gsB29HEx1BLY1jqugsEQXhLPx6SugJvpPKaGyXykM5btaju1AMVCnUQqzrq32rNRVLUaS12Js\n4w/b4gvPUPbH7F9y6HQpIcVqH8fRHIEXXMD9agSdsFiakm1XTDGmPlX3MEEDMEtlyNyMC1nmtYMW\na8fZyrnoWwOF7sNG7JhSY9cdwpHWE1pWKyV867Jm3sfQYDGSYYDBMsQyj+EYvb00AV/DU7Vpei0y\nBF5R+16nO5wVIXDhpvgpozv6qhHk1bhsCptUtPu/L3fhtMmdsJIBpLkRZvIX9CMBv4SQrWn3OtVT\nPsQupTt7r5h2sHic4pU0PaNmmDBJYKyPLlWUIsm6wRSjeDcHqmP6MkvL4cxTDxntHEE75UKMBVIt\nENieEmnIB4zX5x2/rG79Ob228DvZLoawpRXwk1arWNsRllgMAj6Oo3O9dHGuxqJu9L895Kv+Nwgh\n6HCAM4F0DDg5DuySBH7eEoCDRwhnAI7bEex1ATLn7utNx6aEAR6npPruT3+8lL4omRNoiuJZqqKE\nQkYSsIStWG2OXzWCmWdxmNnH0xY9yykGgm0hiNAdjtmbQDCBktC3GBK5E2eeBrDZCyIlm9AMa2yu\n7Q8Q+EibWBMUgGsVpI5i46mliPEWXND4w3kYxwqt6UqEeRmuStDwIul93YeTZlQhpDw4bgdjCRK8\nDmPj1LyjlNIyppETZhbrspgAr8alLPbe+pXqmK4UZnrb8+AsmnMpIUST8yhMYFCeMe7mjF8G4A24\nmH3we6YEiT8AjvkRgxxOJ2eRqifQP0+bmzGbdebwnQ1R++ZZruW777BFujNWshNWsRpB7oF367/F\nkJzh4UKEkml3HcWQu3rNzQmN7d9HCNWIdj1zfY5dl3YjIESfMCqB8+j2OqbVdfSn2xiKE0bhP3lG\nFhM41tKuH/dUlMAl2nGDCbxH+dibRAGm72y0daJqy6wduUUB41dh0Vs3ysyPySAFI9mdgkXL5dWy\n8A+2S4HCllbAT1qtYm1HWAHhM3LNFZUI8Qts60wC5id+lI3eisZ2igDWQgyjmQAPKaDvfnBnqUUA\nfi6/XUFgSwKrMgC/c86oL8cxhx+Ohf3ORsMjm2NkY0vAWhTOl7coeIdibV8uvJSzLaSEAhNqwvqF\nQF9TY5/reBsqy60IKXbFci5DN3PxVRlTXB/gVgCrKN4f0+3v8Pkcr+nfiUBwFTpxMH5gBzSwGkGW\nIv4NwGq7Tnk0VgaHsZjcRlkcF1LCFOZ9ryewJ6R8jRPyS1YgEl6AXo2TbwQV3BtvswwxliHGEXiR\ncZSGCZwC4fW6EeKNVFQALIKb68u1lSPKC3HzNGaNpWICl1nGLk0FNKcQTIZ/wqYGxikTBjheHfMR\nvV/uKykhn4UE3qaETMoo2Bnn2BgFr5OXLJYqtHMzLojqelQizBdwcJgSmrybkmgwTT3DOWu7UYhE\nryZwDbXQC4X+Q18EnVJCXInOfAd78UtswzQCMXWdWzfn2VF9Falximp9TS1kTJrQx+70htl8aT4o\nLP/mAxQmcGqOc/aiUKZMoEw4XQncQi+f3DO0G0lhIjsPqTYvov8H3APacWWUD5fT6KbYGG+015HA\nG1RVEyjv7h4FjN8Aej86nOzOVyihQKdfhzT2SvVeOH2FCPxhuY5VXMMG9P8jYUsr4CetVrG2JZxr\ne/c7oCFMLwg2TeBPyuL7JsXyKQN4pbEoRgAOzdPvJEu/KYnQ9ae25tcBAGrRBbV4F7V4DbXZNGUK\nYPhPurmKfqN8/R1NMag+1iZJ0xsVJ/CiaqsDZRFtwsLA6g5oeKQ/ZmX+hv9wNvqbE9jzU7B7McCJ\nyvCqB7j0e2y2NIhqXokreTQe5z04mSkUPUejRAkFkF5/Ah5kmfYRHkAqDrDgDD2jzT+NMXAyu5wx\ntBmgDQR2Vy2MhKS1T9gen/WnAIOd0kJJAoll6Mbl6Nq4GO6Dt25Vz0hGjcNsiIevOoB02t1VRl1j\nOlOOaEM3LOup9O5GCeGYxlSCwGfGNQ4lMO4BnHhPCRJfq/6uhRSELrM8BxECo33GqyvFi/A1xQCy\npsn7nLtxF6yYZw7nYXjWWZAXMGu8xijGVYHeR5ZAyiI93AsLLo+j1KkFGaHgvnLRBMwv9Bos17QZ\nvdizMCXdvohC9rkPDa8uJWS9JQsHVR9MCZ/No9B25HwvKR7FtKGT5s1hGaRM014wPkYoFB1LaTeG\nvqF4RU16CVK8OYvUNoYSfrQx/Ico82l3Sqg4zSwdiDmOgw3dptJr5Fm9mRTOwOWqXfP+R9Tz5ryn\nMUp1B0dfE6AepnDpmdfTwDwe2nbxFba0An7SahVrO8JNYKRya1saYKWaGFeqF20WgVkxlMWewFG8\nDefGP8QuU4GMzSi7J0e/XeEFoTOAh1LAOhktepEEOBW16IdazEAtbkete7Gh0AqYIRl9AtG/LDOU\nRfE1Zutr/cxmcmppOuxEoC6Ian6KHfgTNmUagSAbM5x4ANzeuMyGmBMfjB9YruaqSoTYD7PnAZwA\n8HSo4scU71t0a3xlubzMu5Qv0S1Z8Bcjtz4Ht989HRs7k2RKjZ85aSaZ9UDEKKGJMp/rL6dkLjn1\n4nSDMkLg3/CQkGZCY3DTSwQ+3BBzGHCdliGQcQp2/+gsfgSeoh0PkmITmJwpi77ZTpBAAZ7V5gg/\ndj/nKZ6AB50fbLUzC0gUYADgy8h+yEQCSL8TR+lgyhfJ0T5jpQ9yaf5+LD0Lv5Lp/QhSwu1vqveq\njuLJ2JziibmfWXD2YjaB3V3rd1cCp9BC3Kr296UY3Gn13GmcS6wB+AOyJMZ/QuNsoxCY+nmyHeC/\nWYw4Y5wTpoT8RlKMMyc0m6QY4gHKh16ucFod3fUASyx6hWjhd1Njrb/HKWbDyU6igo1KwU8XEniU\n3rkhRg2S0C5NEra0An7SahVrO8J9IezatndpietIAQLvEkNZwzb4ktVoYAUirESYxUjON85NAbw1\nR7/bwcMz8xorUcPdMG62WkjDAOdg1NBDUIvFqPX1HhxJf4PKuKAe3BdvZAJILytHdNpZuGMY1wA4\nl0Cf6dg41gNL2BF1rEKII/BCajHWUpMOL4KBtQognerggU81zm1hSCixSLU/+gQ8mHQDrDORf+CR\nmWqya6B4ndbLo+k41XZ9EZLxazH2czXRb2uZaENq35sUMlffUBQls2uBZcwTBDZVR7muvxTx9Hic\nHSfAX9CPG2AuS5BgEVIMuD/aowCvVf3MznF/f2viPTuPWXxKmOKFsBqMqy/cTcZdKCVqUM+ZGOAY\nU7bFcnABbfaH92MoDHCQur4u9KcHIKWwuD4eJRQOtrHMU3xazQXTmTXY4hRD5iR6P2B+oHh3TE/3\ntCaNIHAjs8kxIQLX5Di2gh5+Lt4Md5mtJMDntXNsXyyOkbQbJTN4T+36TGPK2aZobQYoDOQdKeWb\nnmNuok/n/vcy2jDxYUECd1G8Yk6x8p0o5Lg2uoNDKR9dN7Fp7PFRCl3LeGPsC6qw0C5WYUsr4Cet\nVrG2I+wDL34lAzGynMK6gwC+CPCDv+E/t07CqEi1JxU7FdTaSanz19f6CQA8CVJn7l14jKmPCXTn\nq+hCAlFIfbgNcHnpcajFUtT6ly6hhGOW+kxurosajB/0lP4MwBVQae5Gm9tTcERzKOHNMmO/kx4+\nxNnXCwv+0L0sJUjEAI4CgG3xxYnq/3rffxYhZTKd61sIquQGgcCPGPT3tbFwQRFSEYChXpg/J4Qq\nfZFKEfgwx73ezHKvo8h6fx5hdtGLUEIBheCEKilp5baJWksF5yvQGNWrENJJLUmA9ajhAMywjYVT\no+0l+uNTQj4alkLKl9wMYSrXM/H2phA3nsa/HBPCrXpj/qTzMS42G/3jamzqKQaHs2BG1f9fp3Br\njaVgxjpQ8FXTKYbfmL3wjof8UmUQbqOu7RjaQ0/Os9LIpUTx2L3LbE3EMIGLrFchxlQJJfz6GCXc\n+zDFgHvE0lc9JVxnGhLhgkdOWO5NoyJKIzyep5VXLUPRmDVI4HpjvBKUiWk4xTMfU79NpHxoTKTQ\nWJhZly9Z9F+b4q2zzVFOGSGH/84z1zFLvJpWf5dZ3rcGivfOUzxba2co3QavLSzoGHVB9SxWqXP3\noNDd7Gzq1y5NEra0An7SahVrW8IRaqGNQAyhE9FIEsn9IN4ixQeZyXTF0lSpZ27LJCDsxhMgoOP1\njD4ugbdMitq+J7AWx2BodmGsRRFqcS1q8StqHQ9HjisQ/MNkyoKju9MbJ/EF6MUKY32pQCRWjuh+\nRlsb0f01HSbwoLa/lAJYdgCdcwisDbun73oCW6cRCJ6E+xMViLADGtIBpJcD3BHgckho1TIurAe4\nK2VBfY1AKIniuu+x2crzMW6/JIrHW05ammOU9rPoGHbuFWVRPYmycJ9NwcZtAXAsBKfjMTzVeUNo\n94RE1cJTSuCqVej0yW744NcA0quKkZz7DvayhT1Cx+DRZBGSSUNHh3uqFyUebAKEEwTetWhXBPA9\nZA3JEBQovaWEUhrlfLWtS+Gruo1iwN6vxlJPp7+dXgB9Jo7SxZ2xcqnzgVCMBPvit0wQ1c9RFn8/\nT0iMXuLYvehdiBOUUG4PSrbs7gSephgFSYpBUWS0Y/NSziVwuPFOZWgp8+IzXjUU74v5jNUT2Cp/\nC40tXQL3B0UMYGO2GgVX94x2fQ5Fx2d0G0IhqlA+s1mXKbUFCexH4EmKgXoa5ePLJAt1tqBqv4zi\nxfJlvacYNFdSKCA8XCCUuWgEJaHCCTVGCRxhtHMs5QM0TK+Bl6F4s46h4NfK/fRpl2YLW1oBP2m1\nirU9YRmklp5WbZy7wYJz8rIMZBIAp+Rpf7l9bp/LAHrzbGzbWIBzRQWuQy2eQS0+QW3TsU0UXqfX\nKUDO66kI/1ahE0sNSEk1GvgATrzPOP98WgoBG/v1yTFB4BWAn0DLmCxBPL47plxE8SiQAOdiA36B\nbeNL0KNWtbYRwPcB/grBdvxfe+cdJldV/vHvbEmySQjpCYGQQCjSaxAEJNJEQDpIExWk914lq/wQ\nVJogIoKKCCIWwNAJShVIAAkQCRAgBAJppO1O292Z+f7+eM/dOXPuuVN2NtnZ8H6eZ56Uufec9557\n55z3vuctgSKRBbgA4EBK6LS7XfIaRfmpxEI1FmEL1Rcwvlqe4/dGPi9YCuA8eDKeU5RZV8POUrYJ\n6ynbHMF4tVO2JgdSEhcmrf+fR2Cfe3D0pgCnQRT8NMC/288lZTtnR8oWUJu57lfo9YOLLGHiVQ57\nGkpZH3exTHjGlwQyn2GtL/bHFK6Lj7kPHuU8jCGLpwiZS3/OscMYVljaKIv4CooFpZ1hh++znXa+\n8PR5K0Wp+IO53ysoC/omrhxOW6MojvUdpm93DJbSFI2mvAz8xDxbHxD4jqfFRoAPmPufgvi1DfT0\n25eWRZr+LbTLrO83pCTwbCawMwstUW0U69Y/GVaoOigO5BX5sVG256NSrTzneX4uiGhnX4bz3yUI\nrFuJPErFsKcFiKJmBVs94LToeZkps1BlAD4LsERtKy4JtzGf4lbwy/aXsON9BP75yto4B5MxDc24\nF81VJbCso7xtBhP4YgLHHY77PxpgXsSbkOAueI4dqH/TOfc0zyS6zPr+T54B+QjgeCD3aRPimb5I\n8Xv4Q0cWsWTEInObR+q1IH5TCwC+AHCC6e9az/lLKcrK31mZD1VgjUwBXAzQhM6zHpIHLGHu65WQ\nqDi72zaAUckMg0LTHebP35n/H8DwAt9Cye3VRFG6plHyhgWRfEPT6LPR5nhrAsBRZdzn0HNC2WLZ\n51D87XQ4VrkmJPgx1l1Ey/G3VqD4wLiKQ9yzSAYfd0GM+gR+YhMj+l2bhRaqDkqwxrsl2n3caec+\nR/6C0jMUZ/mJLFKPjqJ8BakqbAUuSUlSmaNYwrazzvkRw3nVIkrecCTk5bFoDUSr7Q899yNUYNgc\ne7bn/gWydzCvaCUI3Fikz53Ns9BZM9P6bqA1Dvb9fZB+Z/c0PcorJZrZtRp+TqvGpbJSYE8LEEXN\nClbLmMnqTEp+gqPdH6x15DtF5tIEJEKwrEkJUvst2PLLyUvcFlngR+0A5W3vu3vuivNHpzDpynYg\n+ynAIjXA2AjxCdrAJwOlJIlrvXk5i9hv78HR2TNxE2/B6UyjT46WE6k5dxhF2wsmJyuPFHwWqmBh\n+8pSDD76bWyW+ATruG/67iJziCtz5JUCRzrX0kFjiTKLz0aU1ArlRvk1mEXF2q4Jpb2Iw6mlZj7X\nRcgYoyhJl1K2CoKcUVEKlTcijxJ2HlS9X8wyEhjCSXBK8RNpJbD8CwyN90e8DcjlALIBbdwE/2MW\nseA+FE2kuaqhKIJLrYU3Tsk3NcUzjgmK9cd1Andv2iICv2OR7TFz/64zz2mGYgF1F1z3U1Co2rQz\nkMDDRtZWVlBVwcjwf4yOTMxSFKdQ4AAlb5x7/O+L9DYa4B8APgfwChRY5jtlOYNSSWCeeSaDUlJP\nMCKQhVLaKUr5TZqxeZYyh3j9EylO4AlzfCvlZcNVqraiWOIy5ndyFmVr1KdQJRgRvUop6B5EcH/E\nElZDpVtgTwsQRc0KVqtQrBovMG+BiRP4VcTRV0KsEu5vNIhAK1OZAuRYng3wZaDlMWDE28AWU4C0\n/ICbsS8uHtKOze91fWc29LS1FsAPIJaUJMCHPIuqL8nfUsr21FIzaQfWlFCCwzj6jzoRtz8zHAvj\nA9GyAODxVtuNlO0qe/HKmontQobfUDOULciM6fcKilI71rc4hK5WJvffMF8u5yNW5IxbDnzDc5/n\nojCKLLE7nj6SouDtGbUgeOQPrGjBIjyPnjxOlK1aVzn4tEjLYwHOgPj3rQB4kGmnIFfQm9giMRhL\nPxiCJdwdU/kU9uBdOI7P4uttFL+lK1g8gvEYirXkfQKnexa3jSi+LVcSWH8c5mw6Fh8v6YM018cH\nmT/iu83ljJPV3niKc/cTFN+bmBlv24KUpVgkYpQQ/acpiUF9flMlfZUoW+OB8pQxv5HRb2Oz1y/C\ntblzcT1fxza2YtBKsRKFLIhGprHmU/YcQamEUEyBSxA4PuLcGZ7fXISvHAcB/Ax5d4YEwHuc9n7g\nPItJSsLPrxd77ik+cSsi7kM7RWkdYh2/DiW6sIPyErc/wwplnBGWRU//f/X0m6STM4qybf4A8/5i\nv6rkXilVwZ4WIIqaFaxWMROCz/nUKUXBOkg0XjDp5CAWqz9Bslx3KX8NxJw8BcCfEUxMzTgTk/E5\n1vmPm9wxvj+m3EBxaB2Tb4KPoTAEPwHwNOc6fRaql8x3YyjZ1C9hZC4cngrLYlOHTPoaXPwQJQvy\nYMoi6rNSuWHjHQT+Y/ptYH5xDArYttIT1eOVSByyN+JKMcnzKXQGHpCQrdzfAbwL4tu14AA8FISt\nB5mVExQH8RcpWbN/Qf/2Wx+KleUFiqIw2iMAGPYJCxSHCMsb30Zhlv/EaHy+OcNWmgRFMUndjNPZ\nH/HObPNn4Gaaa5lNIJR1nuLk62br/qH1/dbM14TMpNGnZTCWJvPRnlkOxlLOwJZlWyQ9MqzjGZdA\nliut437kuXYGz5913BBKZOOdhNTB9LTf8RJ2fCCGbGudSWXUhDjvxVH/pCiYR9JRQs2zvSslMWmK\nspA/yyLbe9a5fSn5maKUKVKct73zDiVXXpAZPmN+i+MjejsUoZxozADsZ7X3oqf/J0tdhzl3E4pF\nMbD22W2kKVvzg814veMck2TY3WC5Ge9tCAwu0XcjJeIyeHlL0ROtSUmDYPeTYERSW6XbYU8LEEXN\nClarUEKAXb+LFK28J+bIXRB25m1HZ/RfV5hcD4x7DBjzGvDCWmhGA5rxKzRjJq7oMx5WSD1ANiGR\nuR+HB4kAW9gZ5s1PPfPtnXZPFN+ae5n3oZrHUGHjoiP1qtvH/pgSTIgfUxxRfXmbtqHkxQoitT5g\nZ3ZxwEykrkIbp79O4FGQLPbzAP4YBVt03Q23MItMGmKV+gJgQekdyht0sQUvSWAqu/imS4kicxf2\nJf722A9OdGQdOpK/ximL6FeodvgI4890CyX3R5xvYzOae3KUR6Ypnuucbn3/iN3f/7BJdqCTUmRN\nLON9+E4olL6CcTmY0fmkWqzj9qY/OGBv65iBFCU4sIIEmbBDEWjH4a5sDFlbyeZO+E+Oovj0d2Ss\np5RHcbeckgRuKHF9Q1hY2sf9ZChW2aL54igWzuspyvu4IkdGKVRNVluPOzLkCPyjWP8eeUZQfMpc\npSpJeaG7w/OstlB8Lt3i6sE8mCCwfxl9D6PUoPQ6mNMpNG8+77DbLd+KB/a0AFHUrGC1CiVnk+3Q\n2E7JW+AmwfOF2CcBrt21nl9tAL43F/hqFmhdjr7LluPiIS+iGU+gObCO8SSYqLIGtKe3w6tZpzDq\nu+a4JxG2UJ3pudYYxet9a1acY4jP2NceQ5ZH456CtzlK7b9AAYhTFt+Y+dxLWaRbzfHHGZm2Z3hx\nXE5gB/P9YALX341jX25Ae7tzjZcVl7laOA6yLXsGwFAWZBaPHrPfwNfytV6WBOLXl2C+6v1uEUfG\ngFxBUsuBaOFj2MddBNsInGvOWd/k8Oo8ZE0s45PYK7h/J3jkuc+z6D1jff+S/d18jGJfR6fpjzgf\nxzeLVA0oOSa7MKyE25/DrGMvNfcpS3FUPMhp67uetlKU1AwFlpFD8LdQV1tiRqAQuPXmLmR0Hrg2\nAqHfp3XubSye0T1J4Kwqxi9GyV7+OIG7/orDtgD4uTWHJADe75xjbz8HNe227mL/btLhDkqmeJ+v\nVRvFEhck7FzoOS7BCrdTPTI9zvC2ZPDMjDfHDKLsaGxZTV9KCPa0AFHUrGC1DMUkPc38WB+lP9x8\nOMBlyG8DdQCchaJWEsYAbg2xbg0A2ATwGICnAEc+AWyaBZYQg+cQp21GHPi9JWh2t6+4C8BLz8cv\n/mkcxu0f/AoCm96EsyYBubkQv5k4wMfR9S3IqGvZGZ1157IcgBbOxKb2pHeBmaiPJHANxeeiHgAo\n2x6upSVNMcePpj9B4RhK1Nt7BNLf9eRHHIyl8ykRiBVY2rpxRPK+HsUUqjZWoVCZfjalZKQOPZfM\nZ54eeDUuebYJic4tvH3waOBsHnzaKclXryHwcAsGTq5DR8FLwgC0cj5GkaJk7E6xlGQoVsiJZjGJ\nszAv1NcteU5z7nV8f0yZPgCtbEA7B6CVR+AvqVYMiCzTQbHMzTaL2YN0tt/NNT/geaZshaO/dXxf\nyouTL1jjJIatURmKhelWWkrRP/FtNlmH9kcrr8c5wTmvWm0OKiKbrQQcF3H9z5Y4Nzj/MN/5paCk\nMyjwDzsHN2wN8F6AL0ECZkLzh7n3N1KsXpta/782JW/XhDL7/xMLldWU5x4ECk2g5MQJ/JYSYOGL\n5GynBBt0qcA1xXVgKcNKVYZSKHpzyov3ciPr39iNha+/5LCnBYiiZgVbPeBWED+V5RCLzTcBToc4\nK/8WlokcEjn2X4jpvB0Skm8cx29rEz/becQ6LxHnr0XscDMRFD329Sxbk3FnAllh/i8eR//pG2PW\nrpAs7ivh7YkDzPV01CGT2x7Ts0n0syf3yNIgBI4wsjKLGOdiLBdiRBvFDL8d87XGgkiec8x5+9K8\nzZ6OW1jnvPBvg9eD+mStLNNJtTuh+PLMYnGlKktgzwpaXRuyBbM7SmxpUorKvs58QdncDGzJ3+Ak\n/hPfdpWp4JmZYRYwvoZt2a+z0ox87sAJLabNnShWg5xz/nuUJK530pTocWSKURItLqBYFc4nENsP\nD596JP78xKW4+vctGBiZUoSSRsB+ztMEpnqOq6NETwaJJ11loywlmxKUYVuokgQeMN8NMNcRLLKZ\n23DSFyOwcMVYzOVPcUnwdtVO4B6rzb3oVxDcz78iZLqG0Rnd3ReP75dznU77roUoxSIWs4g2RlN8\nLv9uzl9uZL7IOW4SRWnd2fq/fpQoy0UUxflsj0x23Uz7/zZmcevdEkYk36QofgdTrEw+5XoEJU2C\n2+afKHOUG3TzAqt8WVIA1LDeUrOCrX5wHAp9qpKw6mAB/IObFiWGrJl/1iLwPrH5n3O4cASx4aOE\nWLyeKdqjLFRBUr/FLDR9pxgZxRPZXoySXmBXmoSARY6+CZZPVyPSmbNxQ4KywBZVGAisTyCxGMO4\nJWawCQk2oo2jMP+BDOpsa0eawGTrvANpFLGPMJ5rYhnrze5Nf8T5NHa3J73pxWRYWZgxHEx5e47K\nxD2rzNaCpJsrzJ9PwonWdPp+uMTi4ip2v6alPOyOqQUix5DhofjrUtP2Jp5FzlasZrOLdf4oispB\nlOSZQ5zvIi1GEW2N9xy/nBK48Q7F1+hyFo9E245ibZxr7mOT+f8RFGvM52YsXqQoYEMo+ahazPM5\nh1Z0n/k9+bYk3TxJXh8kisIxlf78Te4nQeDbzvlDKL5sLUa2PZzvfdbic1Am5vpS9Dv8JwlsaI67\ngfl6dwlaAQNOe31YWAcxRXlRcV0B2gkcVeKZbw36d/r4upElSPXwGuWlYDItCyglMtXN37WfZ8yC\n5/IzeiJ0lYpgTwsQRc0KtvrBkxHOst2BTqsCl4V/f1PNHP06sduPiXPGESPfCr5fArDk246ZfAZT\nFBm3gyJZwUPtNFDC0OOUBWghi+Yg4sue+evZCvo7YGu8lrEX8D5It9+BE9xJ+UPrnDWNXBkCnINx\n6dNx82fn4brsq9jOFebjcmVZGVDe2KPqJ84v3QIA8GPn1DhAb8JE0+fCIguL/WmjhIHvGixS72FD\njvL41O+Jp5Km7ZGMzh9EymK9fRnjsgHF2fh+Sl6uYRQlp8V8FtGyJlG2jF1lJGsbJ3wAACAASURB\nVEm/RaGBoqyfRFmEg2f5bM+i6E3AWkTuERQLWxvzSUAPsb7vR8mavgfDDukNFEug/Wy/wvxWadb8\nfcsi/ccoFpXr6Fdc7M9fnHOfYaHSkaAVvUvZtrP9oVpYMgFu57kbsrhCs5ySy2kDhq1saUZHtA4x\nz8nLlIi7tSkvjVnr3E/pzytlfzp8fVCCcHzHBxGtQX2+ekrKjAUEPqGxAFLqSPp+23FG5JBTyoY9\nLUAUNSvY6gePQ7gWXwqd221cXPjdqwSGEw1PEoccQ/xwB2JgwYKWhMkEXrJn8S3ybTP9WfrP+z9Q\n3qjfMJPBfALfADjsPnznJy0YaC86WZo0ChG93onCHFxpgLda/WxD8Zv6Bv1RaAcHySTtzwm4w72G\nj5xrHUdxbp9JsbDMnIux/A7+zJ3xAq/CZexAfSihYk9AUUJ+60z6SQK3l9mCXSyaDWjnd3Df45FH\ny0NVarFNU3KQxcxzM+ctbJ6RYt7ZgtP7I87LcdVDVvtXmwXDt4AWKAQUH6WfEribYkWIEViPhTmI\nEpS3ijb5sfTlLGycWYCRj1nt9KNsrwQh/wkCZ3iufYJZ8IJs9B9TFIldCfzeI+/75d5H074v5cJC\n/7NdcF4dpV5dq3N+grIVeI0Zp40rkOUwSqmWBxlWorP2s09RCEJFlwmc5BxzmXl+HqOTk6mELNeX\neOYS5je7M8O+Ti0EtqigrwmUfGIfUAKForZR3etN00mAy+Lb8q30luYpOH89RitloWhYpSLY0wJE\nUbOCrX5wDYhFIVAyEigoQ8Lz6zvX1VkERnP3/sey7vgdicMOZ11DKOp7OcCdyupZkuWFtkWOwd1B\nqZQswOlNSIyivH11vlndjNPTQC7dF8m2NbCcz2FXu41ihYSHAnwXEl7dAnAmTMoIs4AElefbCPzB\nknV3An/ZDq/OC89Duey1uNBerJOU7ZU0pcxHqAj0IgxfMBwLzdafKAFH4Z7lrDhqsfuhKBXXUCLd\nWt7FRvHd8MycOmSeAXgKSvq28eUYMp1Kp9nWTDG6rMfmFMftII2GT+k5wTln9O6Y+lnMWYMa0caT\ncdu/6eT0olhgzqUo5cEzl6T4j2xN8XPbiLJd1mb1eyUlXN8XIs+X8VWuiaUciBb2QToH0F7w+1Mq\nF1zNiHIpBN7yLKTBgv5nz3czyr2Ppv3XPW2TwB9LnHeb57dJc4+OrESGiPa/btoP8kutoOUMTlFk\n3f5LKgwV9H9LxLgEOZ6OMccNYXjLbgnNdmoX+v0kot+kp59AyRppnf+651m0fyc/KEOG7RhWzHJ0\ntlSVimFPCxBFzQrWO+FRkAzCyyBJHR1nRw6BRMTcCdCJuGHsHNzw3EZ4in0wmj8YsR7XOxu8/Bvg\n8tiAeBMSSed33Yoyc1pRouOW2Ce/gh1SMWTtvFXtfZCeRmvb5l1sVBClBEiYvEnF0EHL+ZeylTKZ\nkvDwK+Z/+wD8GsCdAPahOEW/7JmgcpQ31P2Cyf1Q/DW0xvVFKjUH43ai+Hu8wHyuqqCNRXS2U36K\nS14c4OwIxZDNooivkXzHKyC5tKYALNs6UC6UMhcfm4WFczE20Q/JNPK5oeIAm0u0svYEzE73QZqN\naOPPcGFwkU9RLCYXEyhI02HuwQHMR+S5xXq3sI5dk8Dhe+LJjvAt48slrq8PxarxAEVZCkq8LDfP\nmOvvkybwc4atGcsyqIsPDZdzTAIsu8wHo7d+cpQUHbZlLElg33LbNu1/FNF+kk7yWzP+/6W8BET5\n0bUS2L0SGYrItg3F6vgTepJ1UlKYJJgP9JjBCEftLvQ9kYUKW46SxHYzhhOb7kSxiucoCtE2Xexz\nEP3K0IeUiNAoB/6rrTbGUV4u02ZcOiz5W1hGvilK5LG7DZ5ijZVr6oWwpwWIomYF633w6yj0kUoC\nLHPrppPho4Avvj8BqeEXInfLDphN8Vu6fBomfjYUQc7FXA6yXXhz2dLJxLbETCbJ/THlLjhbRkAu\ncGAnAT6IAznIscI3IcFPsXY7xaw+xrQdOCRnmPf3CNU9o1gtfBMZKXld5gb/fg3bUhQhWW/6IsXH\nsfenVlvbMfymuYJOGPRQfHFCPyQzTncdJRSq26x7mYVYA8dEH185lGzZnZre9TiXfcI+xZFRnAFZ\nxJ5ZjGG5NPoEJ2XMPQz+XEZxxI7RcbSmbEu8z3yE1LGOfCkC2XtxJPtbPrYNaG8DeHIF17oTS6cF\n6KAEPLhZ1SfPxoR7+oXXwBUIvZQUlWFORL85ytbw+pRM9bfSijCroP1H6FeOVtDkSDPH7cHSEXkp\nypbdKstdRImum0xRrrrVekvZ1n+Zsg13TqnrYkQ29wr628XzvOUIfMN87yYdDT4/d9qJUdKGHExx\nI/iEki5nG+e4Hcz3/6L49I0g8JA53t3GnE2pcTismmv8ksOeFiCKmhWs98FfoLD0CAEurKCBNQBM\nxz54As2Yj2bsCiBwWJ3fhsacay0yi/4OJdrNSyhtrSMTJo9COJP7IuYddNNvYotEH6QKlJEmxJlG\nnySBn1nt3ucsJjkCTzh9N5ZYRAJn3s7/m4EteTJ+zRNxO6dje9LahjELoC8f1XpmIjRbURwKcBGQ\nC64jAfC3FN+ZeZSFfAY739wZQ0jRZBJg2UVqy7wXx9uT/nU4j24WclEaSrazDUUxC7ZQ3C2GDCXa\nLGH+/gidCE2KtazO+vc4OttAv8bJHIc5HIu5/B5+X1EdSopy5ttiDO53ksDfzbFfp1gw3s6g7sJ+\nSG4FcC8g5wR05BJjMM9WVDajWDjHR8iwA0W5cZWZBLuYcNJpfz0CvizzKXu8KduLUeMQvIwcQ81Z\n1GXMs+BOlp353czz7v7Ysu6zQ3kJDaL80hT/MbcO5UTnN5c280oxZ/gUxYk9VMdRKQv2tABR1Kxg\nvQOuC9kSegeSX8othDy7zIb6og5TcQTexmTMQnOBj8N6BOILMSKUQRoVvqVbbTal0edX22N6oh+S\nmRiyaaNEBHXJdqa8SR4SQ+ZSKZ8heYf6IsWHcABpRclRrGjupPGK02eM0dsbkZ/XsC1Pwm94Im7v\nuAHnnOG0ebuZ7DrMn7dT8hilKcrDkwQGQYoA3wPwOYCXfIq112a4UO5HsogxBqeEj1HCTkIZUPx5\n7qMoEJ9RfHu2opMygBKV1LllOQfjUk1IdKBwy++aMvucQPFbOpOyjeSOo739kSZwX4n2vkl/MkSa\nBf9b5chltbe5Z4FbTPEd+5DiR+T4yjAGqYOYgFgIE3Jfsiv6IpW9DFcF2zA3ULaygu3EBD3+P5Qt\nzrcoPnfPmM8jtKxH1UKJpp3OQqUqSeA065h/e8b0C8r26xMsM9llN8m7LcVX6DMC97BEOD/lJeZR\n84zdEr5n3nP2pGz7/pWdpa9WLgTOc+5BmsAvnWOGUFIvBM/RFIZfNHzbuG9TtqbXMcfM8hxTKvCD\nFIXr2lUxHqsh7GkBoqhZwWofDgI4H/nyC2mjUKUhyTmTAMtZeOrRhAdxAuZjMv6F5lCenUEE0lnE\nODIctp4AGMqhUlJyWUiSizGUa+Ez9kUqB2Tj5nrGOkcf0og2u4QLB2MpCcy02vsuw1s1vkirP3km\nlmWMCKt+CTtaW025nLneiUZB2mA3PFNPyT11iflzP0eONIH7PXIcwLDCkGRn0j3+DPmIzAykLp8n\nG36o3QaK2d+9ngRli3S0c/wWBJ6nbAP89hL89MAGtD8C8D8Az0UXag9Scii5xaXdsS0STABQnMej\nopzm0nLeBbgxwD0AFn3bppQuCQpCL6ITVeU549sIW1A/+yO++9QsbOwGJrjjnaS12JvrcdMiXF/O\neFYKRUF0x+zP5ru16c8VlWQZKSUqkGEt8xwupWyzh5LoUizVLSzM6RZZvJiSvmIx88p5ksAjJeTY\n1zPuK1WpoliM3PHtoGzD1VFSZtzDfKqD4DlPUTLOx6y2oqxMHRT3iTGeZ6+Szx9W5lisxrCnBYii\nZgWrffgtiIXI/o20QZyZfwQw5ENkzmsC+FWAWwCTYxiJP+FMtOJHuBPNkZXgzyWQ+C+2To3Awlwj\n2jIQK8rRFUstFpQMAZ6D612/nQzAB5wzTkOh8zrrkGEKffdx2j2L8va/gLKo+/IAxSjWiFaKQnMJ\nZcvK3oZpo1huOvbG46G0CZAaYimIcvUWwGFW+9d7Jq1Fdv/mz68x7GPRxk6HdsYAng5JlHkXQkom\nANlKvA3gvwH+5BpcPJB+h3v7jXRKxD05xCw2Qe3CvX3HlYNZNK6lWD0WUqwDvoK/UdFwfSkpJ6IU\nqg4C08zR10BeHJZDFFC7iHAjxQKyDfMlhQZQthPL8JHhOQhvvWaziH0cMbauAjvOkuUnDFtHF3d1\njD1jNoKyTXckJdDAle92c9zujLb8vVKqnzJlqaMkEbWdqJfSKR5O4DiG83dlaFlSKdvi/6bkxPo1\n/dnJ+3tkGEux+Ph8xf7aHddZ5Prv8fSZpWz52rVD2zzPRDuB4VZbvntpX/sVZmzd7+ZY/QTWcl9q\nCs1H1TXY0wJEUbOC1T7cE+GK6+0ABxc5Z12AnyKooTf2gHm4AO24GJeiuaSj5g4ETkqh717r4cO1\nP8R6WzCiEnqJdvqaHzj3w8O+ueIt54xtYDnbx5DJDUTLO5X2W0KmQykKQBsl79BQAgNjyD7vymen\nCQCy7bCKslK2+1zlYSbFKTYoCfI2ZeviAeZ9IxIELqxA4n4A30d+ize5Md6ZGbGAFEy0nmsfTX/Y\nerdkUyYwkH6rSSuBAZ7j9/EsnKEFagiW7IRwotoWgHXm/nVGUFC2Tkpk1g9J8g0U5m3LAZxFie60\nt1TaGFaoltJS2igFj91j5lnfNxH4jRmnF1kkgaZnvCZQrBWBMuzb1r7JHLt+kWfkw1J9lSnPWE8f\ny2kp6QT2piT69SkUO5ln0o3OSzPsd9RBJxqQ4p/0OaMV8gfCUncPFCX+fU+fOYoiXyrJJ2llTafM\nG1HbdzmKlev7zM85OfMsDKVYwu6kbD/2peScu5OiaC1lhaV7lALY0wJEUbOC1T7sC/B/yL9FJwDe\nW+KcpxFsEW76PeLCemLX002eGsYADkYJZ18z2b1vfpgpSkbpIhFr3jZ+QyD+M1xQEL0Fsfz8ynPG\nMcjnq3oDERFvlJD8XdltxYc7+yXAzlxS9qcP0nOt/gdQ/CJa52FM4iTc1r4uPn7ldpyYtrUwygJf\nT7EMnUurWG+Zcu0BR5muR3t2EYYXm6jbCTwcaknGy7VarGBlCQ3XpKRIuIke/yZKXUdXaeswY3UD\nraiuaZh40fG4M7MPHuNNOMtX348EEjFkj3LHAKJgDqWU6eiGhZSTTZutEMvkxpTCz8uYz5z+jrWo\nJcx3OzrXvxZFYQ8eoASB71nf21a8ImHx3ABiFW0HOAfgREo5n2K+gR0Efmz1dS79W5S3VD4+HgnF\nN8htv5XATub7XTzPQqAwtTNfY8/n69XOwtxhoShmiv+dL89TMO4rLQcTJQ+Zb0v1XoqSU2p7rp3A\nQU6bh5rxKMxqK9eyrTlmT0o2+Suo0XurAva0AFHUrGC9Aw4CeC3AByA+LyUUG84DcsQuhxPn1hOj\nHyGkSPLOkFIy7ZAcVpELPCXSpN35YZflMG21UUfgjHY0PPg1vDgLyHWYhWsqwGDbawLA14xCM7MP\n0luswBo/prx9fsJwAsi9mC/lkSTwo0pkKiLt8QDfnYD32w/G30xx3k4lhjvipYIyLQSaZmDL45uQ\nWGGuiw0mT1Mj0jwa93AZ1ky9i42qSIPAPeFs99Yh07EAI+2FKmMWsoRZoD9kQWFUxgD2pSRddS0K\n7TRbNJQts/MpWeVD4ezMW6AC60GCztsvJbAhqs5bkkbRew677j4K83MN5vHqjzhPw68y5p7a1rzj\nAG4B2e6zm1sMMBbRV5nldEJXONQoMrbFaSSlgPYBwZhQtrLHM+z8P4hinRhHKctyJy2lk6JYuzmL\nPIkb2QCxLmetQ1cswMi3Pdeasf5cynAusPUpGfITlEX+HnZT3ifT/o3MbzklKNnD68x3d3nk9fkx\ndjBsnXmXooA/RAmACPn4UbY1XQtnjrJtWFYwA2Wr+IcURaWSaNIZnmt7j+JqEKNYH4uVR2qlR+Gj\nzJeDKRapDynpHyooYK50M+xpAaKoWcFWSxqST+Cg3XM4qYFY4xkaZeUcd3GGvPl7tw4pETnuRPDb\n6gTjIICWMzz7iPLXuXjkmpBILMcg25yVoHmbM4uSO4lWHI5uJq1x9FjcCHyeQl/uhBc5AC0chOUc\ni7mcjQke3xOegPB2FI3iY4pO5zoA/h/ypX82BviKUQqmomidRPaHZL0PnPWTQG5qFrEbKcpQmpK4\ncTjForJt4YLJwyHbWVmAM1/E165iOCrpDuZ9q9rMAvkWncgqiqLl+oO1Osccz+LbHR0E1rgVp84e\n4NzGenTwXWw0jMDRFOvKRKvl0wGm69GR7I94+i844k7maxS6fbxOYBTFmvRdOkWOPfc7Zo67kcDJ\ndDKym2PWoeQI+ppv4aUoou0UBe8zesq3mH58Fp0C/8QBaN0ghqz7TC3/DU66n4UKcZzALyk+R9ey\njASQ3Y25psMpyTxPsseOosi5itJ7DFuVWlmoGEdm4Hf67kPZVrcV/KJRpc75p5pz4kaGu3z3NuLc\nx1hoLWwncJv1/SBKDiqfRTFF2U6uyNqv9AjsaQGiqFnBVjuaMQwXNM7EdxqJxqcTsgjz75CoNVeh\nWg7QGw1DMcXbb9Qhi0T1cFM4EVYD0ZJ9ATu7k1CQO2gEw29+KwgcXnaPwP+ZhS1Bceoc53x/DYG2\nDOo4HdvzBezMOPoXhKRbR5+CsPXE94kDPAKiUC5CXoHsAPj+E9i7P2W77Nu0KsybPkYCvBvgNIDX\nA2wycq5BsaBELALczJEtMwjL5zKsFGUYrsMWJ3C8My5nMGwR6mDeAb/Jc298CtWY23HiEjerfJ34\nrEUuMm9h8+PfwVeSKfQN2llEUb7sRStD2Qpaaq4hTsmIHam0EvgdC60sT7AwV9ae5vsV5s+/sDBC\na1fPwun1U6KUvLGdleewMHfU+osw/BNPnrD4SCyYSNl2z5jrv5U1nEOKElkaFF0OxvZYhq2kKef/\n0ixzu878Bq6hbKWexzKVFIri7z6bcZYZGUhJMBykzohT/CbXco4Z47nWDory3SeqbaWmYE8LEEXN\nCtYboWTvvoIS8WYsTFwHO9xyLC6rn4e9kUD9gH3NoroeZNtnDMJ5j1IAvQ7nFAvOZ9ZC8hSrzCzs\n6WUMnAirfkhm38CWfAa78RHsyyUYkiVwh5GpjuFolyTLLKJKcYS2FYoMgVedY+opPhJLzfctlMzO\nvsLK60CUVOM6VTQtzG8ATkJIqc0lZmHjj0w/K8zkvK4jU4zA98xifh0loeC/KI6pr9FTWxCyhekU\nyc7lkujni6ByFaV2Os7zlMiyNgJ8HN/kSCxgA9pzAJ+/C8ftzHzG86gByFJyMsUXYkTbUHzBOuNq\n1IQEN8as50rcu7kEuAxr8kTczh3xUm4PTP3PDGy5M8XKdot5Zl1fo3ZallUC21Ny+rRQ8lP5/Iy2\ntY5f7HzfSqtcDCXKzHe9vm2qmBmnP1G2ddzUJW8TyF6On7A/WtmINtYhkwR4H4yFk+IQPZHA/nS2\n+GoNAltSilL/jcA3zf8F1tAg+elznh/OS+bYehpLKcUiNcT/O6xIpp3od9hfzgqi4SgK04kU5Wxo\nxDEnmr4C94Rjfcd1J5SXrFMInM4esFquZrCnBYiiZgXrbZiJNElZ7FMEPhmF+adivafTuHBoDtus\nmQPOuC3i7IshW1Qt5s8rSvTV30xAW/kWiO6BtyC/LRVfC/P+NRHTsgPRwibE2Yg0h+CLhwCuaxak\ny5nP1p0mcFbZPUnNN9ePJcuqSmBwM8jW3TtmXINrsbtJA7wM4PauklOPjswCjLRNEh0E/unIfTUt\ny8YL2DmzPabnJmA2L8K1bEfDF+xUrDvP2heh/Eq5RBaxRSzM8fMYJYmiLUOCVmkdStqJBIG2d7FR\n1s6kX4dMdjtMz5pFo5hGOZeWk/IHWJ8H4CFuhf9mv4VHn4bluxRx7xa1o4Gb4e3OFBwNaO8A+BKs\nPFqULVC378fNd6NYuOXkixDLUSweCygWJPeakgROtfpb4mkjW/FT5CSknYo9eC0u6rgM//c7S5mK\nMe8Ttdw8E9+stK9qofiQnWaUiSLRxpHnD6W8FA6jJOJ0x28GpZJCm3lWPzH3qp0STdtlv0RKJKbv\nvscJeNKWhM6vo5T1OZIR2fKd48dS6vqtdOWX4if5hXlGg+LMZdehVEKwpwWIomYF623QqRW2ACPT\nddv+JoMLRhDj16K4VDAFkwDRTMKnmknq5Wtx0akAjwa4XUT7DXRyvpg2hrEbHVqt1mMAD2pE2+QD\n8eCVu+D5W2PIuHmBcgCXvoktbmZesUhRkgmWbTWjZWVxFtAbu+la1oT4Vf3UKDOtRsn6H8CBsvDz\nKeT9ruIH4MGPPZP725bMBb43/8MmBRGT/RHnKfh1G0PbJKwD+IiRIQ7Z/juc4jj+iFmYfkXZqhtM\n8flIUywyh1n9D7L7/x1+wP7h7Tq2oTHSNGcWwrMY9n9bTkjpozLu3U0v46upNcKBXQmAG1jHXctw\nMMV5ZlG7kNH5meyPrVzmGC7svIPpa0TE+e936emRQAzXGnag9f0khrdsV3DV1uLb1siVNLLMo5VT\nqQvtfYuFls0kxTfMFyEYKMH/qaK/Ez1t51iGYkpRph41199inrMZFOtoyQLy7n2i+D7uR9k2rvqF\nlcDvWfjCmCXwaLXtfolhTwsQRc0K1tug9UacjYHH7jWKOHN8DsM2puQVJCG+UcGkf4YzCScYUZSV\n+Tw6GUryyGGUN6x3mc/Dc24ZMo6gmPnfJ/APlqglRUlD8AaBlhNxu1tWJ5jz2q7Bxa6vSguBfYq1\n7fRTR7E8uI2/WW4b5cMxkHQMBwO0LGBsgPhe3QjwmAzqznMm+BSBX1syF0SHXY1LWe/4fa+JZaQk\nB1xEieQyeZ9YB7FUHQ+wrG3R0FWINaJTvodwAF3/p35IusUl3zfXkaUoaAdQlDZ3qyXJMt/cCTT+\nAwffOwCtbhLWBMAJ5pgYZWvaXlTmM791HYSlF1OmfFa2FnM9bQRON30NpD8hY5bi3L42K9wip9QX\nDJLRxs1vKLBOjaUoL25/GYoluQ8lcOASArtUep+LyBQjsDHFJ6qRMi/YY1RVaRNzzbYC20aJbit2\nj1JOG4MJ7MjyLEb9TPtBOpgkgf3KlPVQhpOUBgr4W1H3mxIpuszcq2cp8+rW5j4Hka1T6QmIqAT6\nizG/Vk2bX3LY0wJEUbOC9TYo0SjJeCN40HfAHb7fkEXTxKwYADrnuQRMZm+KMtT5A5uLsdwPD78D\ncVQ/wmrXLd/QRnkbe5Vh5/Ri6RYaTZ/Bqt9OKYcS6YhJcRRPEeCfcEzIAmLWucxkTHa361bQsqaU\nOX43s9CCkWFEZvFVAUVhutvI1G4mVtdC2BnhdR3OyzlZ5zkcCwsWG3ZjUkOKxXIejSLSgXruhP9k\nYsjGgWx7E+L8HX7g3qzbKYkox7HQgfsIFvqU/LBCaRoh+ZnSABlDNr0mls7IIvZvSgTZ3QxbHzIM\nv7UHBbLjlALJweIapz+H0N2UqMJOxZjiYO17UOcyr7xVnI2eksvq2xQFwR67Nxjers6Z/hop6QLi\nFAtOgsCJlY1tgQyjKNvjP6PUDAyy679Lx0IejE8VffnyUJVSej+2zt+VovAuN/fwJ2X02Y8S2XkW\nTbkcSlLMUrn5zma0n2ALnbxk5pxtnWey3VzzTBYqpnE6KWIqheI75b48d1NamS8l7GkBoqhZwXob\nBJpmDcPftz4Z2SMPQXLdevwX2PBZIGP7Rh1kHd+Zv+ZzjOZQfGFlAc8ltsSMaynbQFcz/Ha+jOEw\n+DYCFzgyDaFJQ0B5k3UXmhZajr6ea3ogODYH8HTcwrrQ2sHEdGz/FvMLXs4sXBVVUqe8Hc5hPmHj\nIlpvthRLwL6sIOFld0CJWIpKYdGXsg3y7lyMfbEeHctiyGYAsg9SmVtweugeldHfOMrb8nyKEhdp\nKSKwEcWRO0vgs8UYthvAY7bDqze9gK/lJmMyN8VM7oLnOQ0TySK11yiL9dfYZT8YrrkZ3p6yM17I\nnI0b2hJosq1KaYb9Y3wWp5cJNBPY38j0DYoldw/Ps0s6BW/NOT9kePst5zk/zi4mYaRYVH/G6Izy\nKygBCod4+s2yC/XszP1ZaH737ti1UepB2pbGBIEjSrcc2d9LEdfmjmvgExSn2SamWM9cH7bOLdkK\nrne6Ga8UI3Ltmb52ZPRWZAtNUlPnvHMZjn5tpz8paUll0LTZSE9FACPjT81YpSn+H5qeoeuwpzre\nB8C7AGYDuNjzfY8JttrRjG3RjE9x6qY3ARP+DQz4F4BGSEj+ZvJnHoqZOkGAv8D5IevGMCzOmYnk\nVYa3ZGYxvM3QSlncTyawIcVnJUhD8AHFhO9OOnF6CqdaMl7gnJP+FGP+DPA6gLPq0TH9YlxzJiUk\nfgpFCXqDFeafsvobQOAgAofRitChbE0FDr8JAj+voM0mSlj8o5S91yoc3Uv2NgaSQuHui3DtL+nx\nqylD1nnMWzw6KFndi4ZzM+wDMvZs3Ji1fboGoJX34/ALotqoBkq4+kWeBcr92NbRVhZanRIU5Wld\nihVmMi3HXYrCYLeVInC2Rxa36G+KEnnpLpSBhfZWeurRlbje8z331v5NHWKOOyHiuARLFocO9Xkl\ni+cSm03JCB785i+tpH1Pf27Bc1eJy1B8lPakWDjHWueuwbAC3WqekSaK/9/1lOjSJyhZ/sc7/T/v\ntJGkJOZ8i1IRoJ85L2HG5TXmLZyBrG2UuTL0+6Eo7q6MXxiZ7P+Ps4woQ0pQTof5TKNmTF+ZsCc6\nrQfwAeRBbQQwA+HIgh4RbLWjGQeiGYux8zVTgDM6gB0zQDwB8IBip1EUykyM5QAAD+9JREFUkftP\nxa2vB1m9g4/xvwl+0HOYd7hspbyR7cZ8Hh77u8BHxjXPf07xYwkmyaSZPOoA1kPyKtU78jVQfK3S\n5vhpNE6eFEvKfKv/V+gknewOjAyuIpikFe1W5Nw6SrK+pHXe8wTqhmPRgH5IngLwfIBl124rl/ex\nwRqX46ol6+HD3CaYyX/g4DStKLQIeXegP8HijynbW5f5x5hHAXwcEsa/KQD0RdIpaN2RA1h0kaW8\nSR9LUY7vdBe5iHMmMZ98tJgylWW+SGyKshC/ac5NU7ZPN6IozR3m2DhNIlGKtSrB/JbdO/TUIjTH\nbk2xbnxEKbO0LqO3hAKFa2uakkmUF5I3jVyz6bwgmGfdbSfIjP8481nJN/Q8u4FyErKulRjn64qM\nbTvzOeG6zRGeohDOpCgxP7OupZ2ifESVoIoxnNYiUCRXULKN289LljJ/bUrJwP4h/RbMYE5LMr/l\nac8Jt1G2Zm+mzFV30pM6gWKJde9LG6Vg9FoUJSxlrvOaMsZpPxYqzu00EazKSoE90elOAJ6w/n2J\n+dj0iGCrDc2IoRkXoBnzsPf53wN+3C47a50pmRKukuKHG8MK2++POM/GDfaP/WZKWoajaeUwoWyD\nHUZ5YytVmJeUHFkXUxavSwn0Bbg7JAdTCuI0v1tIOvFTGctC35EnWeg7kiRweXcNrdXPSPoX65Jp\nGSjbLq6FIP4J1jlzfczO9kecjWjLxZBNASyrLEYFkl8G5Doza9dJhOSkEvJu7pnoMyxUgl9lgZMs\nT0M+OjEHiR7cEJLx3W4qDfD8Ev1fYI1XhrK1XHQLkKLYlHrugjpx9jW9SFF4x9MkX6REQ7kvAs9Y\nfW1EiYw9lhHKO8VHbA7zzuqnmv8/g/kIOJ+MgYP7XRRn+UCOnBmHwVYfU1i44AfBIt+iExVGKcnk\n2+68qdi4eq7LrcGXNe22UIINRlbSXlcg8FWK5ftHBEaXOHZH5h27Sz0fwZjMKHJ/fMe7/zenzOvw\nVYUPFPi9zHM5hsCg0q0BlO28kFtGOecqXYI90elhMIkXDcciXICzRwRbLWhGI5pxB5oxA80YCxx6\nBzA+51SGSQMsM3SZEwE+vz4+SFyJydkM6joVAJZwZKVYMIpmrzSf6c6ZQxDKicQWONuTEX1+5Gn/\nnvKutXzM5ObLT/O3Ms7dyjOhx2/E2e1NIb0lN7dUexVKPttzC+4oeoa82T9iLZwJhhWMFgK7WWd9\n4vSRBXgVwLOQV7QykFqRRcrpAAz7vbQRKKWE+aIz0xTlZCpFeX/Kc8wiT1sPeY77b/FxDrXxP0an\nU/gKZaun2KKdZNiatdwec4olpcWMT5qicE0oItMJ1j0NnO4jt9qLtHOo+d0tpGy3bUWp9ViTGb4p\nEZenMbpYsvvxKV9BXj+f47/7ojWtTLmeLCJDCyuPAj2NHreMro2aUgbsiU4PhSpUK4dm1KEZT6EZ\nD6MZAwEcDjQsBN5zy50sRGetuPKgFE793ExCCQL/ZAkHRkpB0iinTHsCcpyS+VWIVco+dAXASEd1\nq8/7GfaBOb2Say0Xhv1nSOD+Ms5rNAtsIGcbgU8ux1XpmDM/x5Bt6Wap3/IoOiXzalG2OE+h5KI6\n37O4r2BBbh7Oc/rJATTbFDwc4P0Afw2wnOSIbi6odvp9L+1z7mI4X9H5tLLKM1xvsIOW5ck67gjn\nOU7QyQxfQpY6hl8sErTKE1F8b95jtL9XjuHFO0EnGIKy5X0exbm5ZIoJAkdRFMsHWSQQZHWDYlV0\nlY2oMX7Pc9w081x8bP2OE+a5+9Q8V4HlcfsyZQp8MqMU6ooCMyjBKdNY6HpRceCBUjbsiU53ROGW\n36UIT44E0Gx9Jq18sVYTmjEJzagHsBfkbXtrgD+AWKUSkC2XLk2clPw1X6VsWZVbGPSUiEWiw/z/\nCoZKoXAd+MveFLVkmP6GULJfJ81Edy9XUuSKWbTcsONyc9QMpZQUecv8+c3nsGvSdtjuiyTr0fGP\nbpZ6f+QtRFmjqEZaMSJkjzHvbBu8rS9kwVYEL0Jhlvc4up7b6hcMW1I2KHFOf0pepjRFITvFc0yd\neT5SZsGZw4js15Stuc8pAQ5XscLEivSXpNnfOWYwxSn6YRZu79Fc8xTmUx3EjeyrLEnn6gbFGT1I\ny5GgRGLeR/HBbDP//1PmfZsCx/I4jfM+JQr4l+benGWeqUEUZf00Gv+3CmQ6jOEUCcELS8V5pygv\nb/tRFOeaLj3UC5mEQj2lRxSqBkgx0PEQk7A6pXc/OwBYjIL8T+wPcF2UKNmxMjAL8L6UfCrPUnxN\nzqTkafHWBkS+7M0K8+d5FfRXR/GtWqn+G+a6Lqa8pb7PMqrel2jr3j/guNQQLGFfpLgxZr0BMBTu\nXD3cFVIr8AaA63epBVFc7zfX/i8CTjuMQfyoXgH4JMCJXZZW7udllEjNp9nNlhSKv9TmXIlbVBQf\nGDtY46/FlCFKcsyFzOeoutv6HV1C2WZTZapKCGxACUQoWseOsoV5C4Eb6a2F2e1ynWkU/RVG2Z+0\nsvtUqqbH9JZvAXgPEu3ni/BRharrbAJgAYBv97Qg1cMtINtDFft19EbMgvlNSrmLL832y5cFo+Qf\nQnHkLqkMUaxs2xPYcFXIp9QWlJxX27BMJ3Slx6lZvaVmBatx6gHMBHBcTwuiKIqiKF8ialZvqVnB\negFdLjyqKIqiKEqXqFm9pWYFUxRFURRFceiS3lJRdIuiKIqiKIoSRhUqRVEURVGUKlGFSlEURVEU\npUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEU\nRVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEU\nRVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagU\nRVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGF\nSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakS\nVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGU\nKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEU\nRakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEU\nRVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIU\nRVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUq\nRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpU\noVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGq\nRBUqRVEURVGUKlGFSlEURVEUpUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKlGFSlEURVEU\npUpUoVIURVEURakSVagURVEURVGqRBUqRVEURVGUKqlGoTocwP8AZAFs2z3iKIqiKIqi9D6qUaje\nBnAwgOe7SRbFz6SeFqAXM6mnBejlTOppAXo5k3pagF7MpJ4WoJczqacF+DJSjUL1LoD3u0sQJZJJ\nPS1AL2ZSTwvQy5nU0wL0cib1tAC9mEk9LUAvZ1JPC/BlRH2oFEVRFEVRqqShxPdTAYz2/P9lAB7u\nfnEURVEURVF6H7FuaOMZAOcD+G/E9x8AmNAN/SiKoiiKoqxsPgSwQaUnlbJQlUsxxaxioRRFURRF\nUb4sHAzgUwApAAsAPN6z4iiKoiiKoiiKoiiKoiiKYSjEmf19AE8BGOw5ZizE9+p/AGYCOGuVSVeb\n7ANJQzEbwMURx9xsvn8TwDarSK7eQqnxOwYybm8B+A+ALVedaL2Ccp4/AJgIIAPgkFUhVC+hnLGb\nBOANyFz37CqRqvdQavyGA3gCwAzI+H1/lUlW+/wewEJITsgodN2IptT41cS68XMAF5m/XwzgWs8x\nowFsbf4+EMB7ADZZ+aLVJPUQx/3xABohE4c7FvsCeMz8/asAXllVwvUCyhm/nQCsaf6+D3T8bMoZ\nv+C4fwN4BMChq0q4GqecsRsMeXFcx/x7+KoSrhdQzvg1A7jG/H04gCXoPt/f3s6uECUpSiHQdaM4\npcav4nVjZeShOgDAH83f/wjgIM8xCyA/HgCIA5gFYMxKkKU3sANkUvkYQAeAvwA40DnGHtNpkEl6\n1CqSr9YpZ/xeBrDC/H0a8oubUt74AcCZAP4OYPEqk6z2KWfsjgbwDwDzzL+/WFXC9QLKGb/5AAaZ\nvw+CKFSZVSRfrfMCgGVFvtd1ozilxq/idWNlKFSjIGY0mD9L3cDxEC1x2kqQpTewNsS5P2Ce+b9S\nx6hSIJQzfjYnIP/WppT//B0I4Dbzb64CuXoD5YzdhhA3iGcAvAbgu6tGtF5BOeN3B4DNAHwO2X45\ne9WItlqg60b3Uda60VXTaVTCz8udfxPFJ9+BkLfesyGWqi8j5S5ObmoKXdSESsbhGwCOB7DzSpKl\nN1LO+N0E4BJzbAzdk79udaCcsWuEFI/fA0B/yFvvKxC/li875YzfZZDdjEmQfIZTAWwFoHXlibVa\noetG9ZS9bnRVodqryHcLIcrWAgBrAVgUcVwjxBR+D4CHuijH6sBnECf9gLHIbw9EHbOO+T+lvPED\nxKHwDsheeDEz75eNcsZvO8h2DCB+LN+CbNFMWenS1TbljN2nkG2+lPk8D1EIVKEqb/y+BuBq8/cP\nAcwBsDHE2qcUR9eN6unxdePnyEdrXAK/U3oMwN0AblxVQtUwDZCJYjyAPijtlL4j1LnQppzxWxfi\nq7HjKpWsd1DO+Nn8ARrlF1DO2H0FwNMQB+z+EAfYTVediDVNOeN3A4DJ5u+jIArX0FUkX29gPMpz\nStd1w894RI9fTawbQyETiJs2YQyAR83fdwGQg/yA3jCffVatmDXFtyCRjh8AuNT838nmE/Ar8/2b\nkC0EJU+p8bsT4swaPGvTV7WANU45z1+AKlSFlDN2F0Ai/d6GpohxKTV+wyF1Y9+EjN/Rq1rAGuY+\niG9ZO8QSejx03aiEUuOn64aiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqiKIqi\nKIqiKIqiKIqiKIqiKIqiKIqiKIqirAr+Hw46nd/nzZLbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10938d210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logreg = linear_model.LogisticRegression(C=1e30)\n",
    "logreg.fit(data[['f0','f1']],data['Y'])\n",
    "\n",
    "def plot_dec_line(mn, mx, b0, b1, a, col, lab):\n",
    "    '''\n",
    "    This function plots the results of a bivariate logistic regression as a separating hyper-plane\n",
    "    '''\n",
    "    x = np.linspace(mn, mx, 1000)\n",
    "    dec_line = map(lambda x_i: -1*(x_i*b0/b1 + a/b1), x)\n",
    "    plt.plot(x, dec_line, col, label = lab, markersize = 2)\n",
    "    \n",
    "\n",
    "    \n",
    "#Now we'll plot the data, the fitted curve and the actual line\n",
    "plt.figure(figsize = (10, 10))\n",
    "plot_dec_line(0, 1, logreg.coef_[0][0], logreg.coef_[0][1], logreg.intercept_[0], 'black', 'Fitted')\n",
    "plot_dec_line(0, 1, beta[0], beta[1], alpha, 'green', 'Truth') \n",
    "plt.scatter(data['f0'][(data['Y']==0)].values, data['f1'][(data['Y']==0)].values, color='r')\n",
    "plt.scatter(data['f0'][(data['Y']==1)].values, data['f1'][(data['Y']==1)].values, color='b')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The nice thing about simulations is we know the truth and we can compare our learned model to the truth.  This is incredibly useful \n",
    "\n",
    "way to study the phenomenon of overfitting. In the above example we can compare the truth (that we created of course) to best answer\n",
    "\n",
    "given by the data.  Sometimes the fitted vs. truth lines don't match exactly. In extreme cases they are no where near each other.\n",
    "\n",
    "Let's see how the number of records affects this phenomenon.\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAGqCAYAAAAWWuWTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFqGv/AIiZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1093d0590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_a_fit(alpha, beta, n):\n",
    "    '''\n",
    "    Generate a dataset and return a fitted model to it\n",
    "    '''    \n",
    "    dat_n = gen_logistic_dataframe(n, alpha, beta)\n",
    "    lr = linear_model.LogisticRegression(C=1e30)\n",
    "    return lr.fit(dat_n[['f0','f1']], dat_n['Y'])\n",
    "\n",
    "#Now get a few models with different sample sizes\n",
    "ms = [ get_a_fit(alpha, beta, 10**k) for k in range(1,7) ]\n",
    "\n",
    "#Now let's plot these against each other \n",
    "fig = plt.figure(figsize = (12, 6))\n",
    "for k in range(6):\n",
    "    ax = fig.add_subplot(2,3,k+1)\n",
    "    plt.title(\"n={}\".format(10**(k+1)))\n",
    "    plot_dec_line(0, 1, ms[k].coef_[0][0], ms[k].coef_[0][1], ms[k].intercept_[0], 'black', 'na')\n",
    "    plot_dec_line(0, 1, beta[0], beta[1], alpha, 'g', 'na')\n",
    "    ax.set_xlim(0, 1)\n",
    "    ax.set_ylim(0, 1)\n",
    "\n",
    "fig.tight_layout()\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Look at how much the black (fitted) line varies from the green (truth) line as we vary the size of the sample. With n=10, the fitted separating plane is nearly perpendicular to the truth. We only visibly fit the truth exactly when n=1 MM (though we come very close with a few orders of magnitude lower).  The lesson here is that with more data our fitted curve is expected to look more like the actual truth. Each realization of the green curve is a single estimate from one subset of some theoretically infinite data set. The fitted curve is essentially a function of the data. If we expect randomness across datasets (an artifact of sampling), we also should expect randomness in the curves we fit. The plot below illustrates this.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe4AAAHfCAYAAACWMTteAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIkSZIOKf8/q4CPJb5X390AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aed2fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (8, 8))\n",
    "\n",
    "ax = fig.add_subplot(111)\n",
    "for k in range(50):\n",
    "    try:\n",
    "        '''\n",
    "        I found that with small datasets of size=10, sometimes you generate a dataset with only 1 class.\n",
    "        This helps us get around that problem when it happens.\n",
    "        '''\n",
    "        mod = get_a_fit(alpha, beta, 10000)     \n",
    "        plot_dec_line(0, 1, mod.coef_[0][0], mod.coef_[0][1], mod.intercept_[0], 'r.', 't')\n",
    "    except:\n",
    "        continue\n",
    "        \n",
    "plot_dec_line(0, 1, beta[0], beta[1], alpha, 'k', 't')\n",
    "ax.set_xlim(0, 1)\n",
    "ax.set_ylim(-1, 1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The black line here shows the truth. Each red line is a line fitted against a single realization of the data. Most are close to the\n",
    "\n",
    "truth, and it looks like E[red line]=black line. In real world situtations though we only get one data set. When your data is small\n",
    "\n",
    "(and model too complex), you might get unlucky and it up with a line that is very different from the theoretical truth. The red lines\n",
    "\n",
    "that are far off from the black lines are examples of unlucky overfitting. In real applications we'll likely never know the true \n",
    "\n",
    "underlying data distribution, but with the techniques taught in this course, we can at least be confident that overfitting can be \n",
    "\n",
    "avoided.</p>\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
